Question 1

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$.

Accepted Answer

A)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } + 5 } { 5 }$ 
B)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } - 625 } { 125 }$ 
C)  $( f \circ g ) ^ { - 1 } = \frac { \sqrt [ 3 ] { x + 5 } } { 5 }$ 
D)  $( f \circ g ) ^ { - 1 } = 5 x + 5$ 
E)  $( f \circ g ) ^ { - 1 } = 5 \sqrt [ 3 ] { x + 5 }$ 
A)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } + 5 } { 5 }$ 
B)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } - 625 } { 125 }$ 
C)  $( f \circ g ) ^ { - 1 } = \frac { \sqrt [ 3 ] { x + 5 } } { 5 }$ 
D)  $( f \circ g ) ^ { - 1 } = 5 x + 5$ 
E)  $( f \circ g ) ^ { - 1 } = 5 \sqrt [ 3 ] { x + 5 }$

Question 2

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$. $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Accepted Answer

A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C) 
$g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$ 
A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C) 
$g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Question 3

Find $f \circ g$.
$$f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$$

Accepted Answer

A)  $( f \circ g ) ( x ) = 3 x - 17$ 
B)  $( f \circ g ) ( x ) = 3 x - 7$ 
C)  $( f \circ g ) ( x ) = 3 x ^ { 2 } - 17 x + 10$ 
D)  $( f \circ g ) ( x ) = 2 x + 3$ 
E)  $( f \circ g ) ( x ) = 2 x - 7$ 
A)  $( f \circ g ) ( x ) = 3 x - 17$ 
B)  $( f \circ g ) ( x ) = 3 x - 7$ 
C)  $( f \circ g ) ( x ) = 3 x ^ { 2 } - 17 x + 10$ 
D)  $( f \circ g ) ( x ) = 2 x + 3$ 
E)  $( f \circ g ) ( x ) = 2 x - 7$

Question 4

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 6 | + 2$, where $x > - 6$

Accepted Answer

A)  Domain: $[ - 6 , \infty )$; Range: $[ 2 , \infty )$ 
B)  Domain: $( - \infty , 2 ]$; Range: $[ - 6 , \infty )$ 
C)  Domain: $[ - 6,2 ]$; Range: $[ - 6 , \infty )$ 
D)  Domain: $( - \infty , - 6 ]$; Range: $[ - 2 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $[ - 6 , \infty )$; Range: $[ 2 , \infty )$ 
B)  Domain: $( - \infty , 2 ]$; Range: $[ - 6 , \infty )$ 
C)  Domain: $[ - 6,2 ]$; Range: $[ - 6 , \infty )$ 
D)  Domain: $( - \infty , - 6 ]$; Range: $[ - 2 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question 5

Hooke's Law states that the force $F$ required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$, where $k$ is the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied.
$\begin{array}{|c|c|}
\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \
\hline 20 & 2.8 \
\hline 40 & 5.0 \
\hline 60 & 8.0 \
\hline 80 & 10.6 \
\hline 100 & 13.2 \
\hline
\end{array}$

Find the equation of the line that seems to best fit the data. Use the model to estimate the elongation of the spring when a force of 50 kilograms is applied. Round your answer to one decimal place.

Accepted Answer

A)  $13.2$ centimeters 
B)  $9.9$ centimeters 
C)  $3.3$ centimeters 
D)  $6.6$ centimeters 
E)  $5.0$ centimeters 
A)  $13.2$ centimeters 
B)  $9.9$ centimeters 
C)  $3.3$ centimeters 
D)  $6.6$ centimeters 
E)  $5.0$ centimeters

Question 6

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$.

Accepted Answer

A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$

Question 7

Find all real values of $x$ such that $f ( x ) = 0$.
$$f ( x ) = \frac { - 2 x + 5 } { 5 }$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\pm \frac { 1 } { 2 }$ 
C)  $\pm \frac { 5 } { 2 }$ 
D)  $\frac { 5 } { 2 }$ 
E)  $- \frac { 5 } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\pm \frac { 1 } { 2 }$ 
C)  $\pm \frac { 5 } { 2 }$ 
D)  $\frac { 5 } { 2 }$ 
E)  $- \frac { 5 } { 2 }$

Question 8

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 ) \quad$ line: $- 5 x - 15 y = - 6$

Accepted Answer

A)  $y = \frac { 1 } { 5 } x + \frac { 39 } { 5 }$ 
B)  $y = - \frac { 1 } { 3 } x + \frac { 17 } { 3 }$ 
C)  $y = 3 x + 19$ 
D)  $y = - 5 x + 27$ 
E)  $y = 3 x - \frac { 5 } { 3 }$ 
A)  $y = \frac { 1 } { 5 } x + \frac { 39 } { 5 }$ 
B)  $y = - \frac { 1 } { 3 } x + \frac { 17 } { 3 }$ 
C)  $y = 3 x + 19$ 
D)  $y = - 5 x + 27$ 
E)  $y = 3 x - \frac { 5 } { 3 }$

Question 9

Evaluate the following function at the specified value of the independent variable and simplify.
$$f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$$

Accepted Answer

A)  12 
B)  0 
C)  4 
D)  16 
E)  undefined 
A)  12 
B)  0 
C)  4 
D)  16 
E)  undefined

Question 10

Find the inverse function of $f$.
$$f ( x ) = x ^ { 9 } - 2$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$ 
A)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$

Question 11

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$$\begin{array} { l } 
L _ { 1 } : ( 7 , - 4 ) , ( - 9 , - 1 ) \
L _ { 2 } : ( 4 , - 6 ) , ( - 3,9 )
\end{array}$$

Accepted Answer

A)  parallel 
B)  perpendicular 
C)  neither 
A)  parallel 
B)  perpendicular 
C)  neither

Question 12

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$$

Accepted Answer

A)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$ 
B)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$ 
C)  $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$ 
E)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$ 
A)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$ 
B)  $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$ 
C)  $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$ 
E)  $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$

Question 13

Find all real values of $x$ such that $f ( x ) = 0$.
$$f ( x ) = 49 x ^ { 2 } - 64$$

Accepted Answer

A)  $\pm \frac { 7 } { 8 }$ 
B)  $\pm \frac { 8 } { 7 }$ 
C)  $\pm \frac { 64 } { 49 }$ 
D)  $- \frac { 64 } { 49 }$ 
E)  $\frac { 8 } { 7 }$ 
A)  $\pm \frac { 7 } { 8 }$ 
B)  $\pm \frac { 8 } { 7 }$ 
C)  $\pm \frac { 64 } { 49 }$ 
D)  $- \frac { 64 } { 49 }$ 
E)  $\frac { 8 } { 7 }$

Question 14

Find $f \circ g$.
$f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

Accepted Answer

A)  $( f \circ g ) ( x ) = - 4 x - 25$ 
B)  $( f \circ g ) ( x ) = - 4 x + 10$ 
C)  $( f \circ g ) ( x ) = - 4 x ^ { 2 } - 25 x + 21$ 
D)  $( f \circ g ) ( x ) = - 5 x - 4$ 
E)  $\quad ( f \circ g ) ( x ) = - 5 x + 10$ 
A)  $( f \circ g ) ( x ) = - 4 x - 25$ 
B)  $( f \circ g ) ( x ) = - 4 x + 10$ 
C)  $( f \circ g ) ( x ) = - 4 x ^ { 2 } - 25 x + 21$ 
D)  $( f \circ g ) ( x ) = - 5 x - 4$ 
E)  $\quad ( f \circ g ) ( x ) = - 5 x + 10$

Question 15

The average lengths L of cellular phone calls in minutes from 1999 to 2004 are shown in the table below.
 $\begin{array}{l}
\begin{array}{|l}
\hline \
\text { Year }\
\hline 1999 \
2000 \
2001 \
2002 \
2003 \
2004\
\hline 
\end{array}
\begin{array}{|c|}
\hline \text { Average length, L } \
\text { (In minutes) }\
\hline 2.38 \
2.56 \
2.74 \
2.73 \
2.87 \
3.05\
\hline 
\end{array}
\end{array}$

Use the regression feature of a graphing utility to find a linear model for the data. Let $t$ represent the year, with $t = 9$ corresponding to 1999 . Use the model to predict the average lengths of cellular phone calls for the year 2015 . Round your answer to two decimal places.

Accepted Answer

A)  $4.37$ minutes 
B)  $8.74$ minutes 
C)  $5.37$ minutes 
D)  $3.37$ minutes 
E)  $2.19$ minutes 
A)  $4.37$ minutes 
B)  $8.74$ minutes 
C)  $5.37$ minutes 
D)  $3.37$ minutes 
E)  $2.19$ minutes

Question 16

Algebraically determine whether the function below is even, odd, or neither.
$$f ( q ) = 2 q ^ { 3 / 2 }$$

Accepted Answer

A)  even 
B)  odd 
C)  cannot be determined 
D)  neither 
A)  even 
B)  odd 
C)  cannot be determined 
D)  neither

Question 17

Determine algebraically whether the following function is one-to-one.
$f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$, where $x > 0$

Accepted Answer

A) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { not one-to- } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
\pm a & = \pm b
\end{aligned}$$ 
B) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 } { 3 + 6 } & = \frac { 5 } { 3 + 6 } ; \text { one-to- } \
\frac { 5 } { 6 } & = \frac { 3 } { 6 } \
a & = b
\end{aligned}$$ 
C) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } ; \text { one-to-one } \
\frac { 5 } { 3 } & = \frac { 5 } { 3 } \
a & = b
\end{aligned}$$ 
D) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 9 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 9 b ^ { 2 } } \
\frac { 5 a } { 9 } & = \frac { 5 b } { 9 } \
5 a & = 5 b \
a & = \text { one-to-one }
\end{aligned}$$ 
E) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
a & = b
\end{aligned}$$ 
A) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { not one-to- } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
\pm a & = \pm b
\end{aligned}$$ 
B) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 } { 3 + 6 } & = \frac { 5 } { 3 + 6 } ; \text { one-to- } \
\frac { 5 } { 6 } & = \frac { 3 } { 6 } \
a & = b
\end{aligned}$$ 
C) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } ; \text { one-to-one } \
\frac { 5 } { 3 } & = \frac { 5 } { 3 } \
a & = b
\end{aligned}$$ 
D) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 9 a ^ { 2 } } & = \frac { 5 b ^ { 2 } } { 9 b ^ { 2 } } \
\frac { 5 a } { 9 } & = \frac { 5 b } { 9 } \
5 a & = 5 b \
a & = \text { one-to-one }
\end{aligned}$$ 
E) 
$$\begin{aligned}
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } + 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } + 6 } \
\frac { 5 a ^ { 2 } } { 3 a ^ { 2 } } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 b ^ { 2 } } { 3 b ^ { 2 } } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 5 } { 3 } + \frac { 5 a ^ { 2 } } { 6 } & = \frac { 5 } { 3 } + \frac { 5 b ^ { 2 } } { 6 } \
\frac { 30 + 5 a ^ { 2 } } { 18 } & = \frac { 30 + 5 b ^ { 2 } } { 18 } ; \text { one-to-one } \
30 + 5 a ^ { 2 } & = 30 + 5 b ^ { 2 } \
5 a ^ { 2 } & = 5 b ^ { 2 } \
a ^ { 2 } & = b ^ { 2 } \
a & = b
\end{aligned}$$

Question 18

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$$

Accepted Answer

A)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 2 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x + 9 ) ]$ 
A)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 2 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $g ( x ) = - \frac { 1 } { 2 } [ f ( x + 9 ) ]$

Question 19

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Accepted Answer

A)  $y = 4 x + 23$ 
B)  $y = 4 x - 2$ 
C)  $y = \frac { 1 } { 4 } x - \frac { 23 } { 4 }$ 
D)  $y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }$ 
E)  $y = - 4 x - 10$ 
A)  $y = 4 x + 23$ 
B)  $y = 4 x - 2$ 
C)  $y = \frac { 1 } { 4 } x - \frac { 23 } { 4 }$ 
D)  $y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }$ 
E)  $y = - 4 x - 10$

Question 20

Find $f \circ g$
$$f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$$

Accepted Answer

A)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } + 6 x }$ 
C) 
$( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } + 1 } { x ^ { 2 } - 9 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 9 }$ 
E)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 23 } { x ^ { 2 } - 9 }$ 
A)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } + 6 x }$ 
C) 
$( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } + 1 } { x ^ { 2 } - 9 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 9 }$ 
E)  $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 23 } { x ^ { 2 } - 9 }$

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Find $f \circ g$ . $f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 6 | + 2$ , where $x > - 6$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 2 x + 5 } { 5 }$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 ) \quad$ line: $- 5 x - 15 y = - 6$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$

Find the inverse function of $f$ . $f ( x ) = x ^ { 9 } - 2$

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither. :(7,-4),(-9,-1) :(4,-6),(-3,9)

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Find $f \circ g$ . $f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

Algebraically determine whether the function below is even, odd, or neither. $f ( q ) = 2 q ^ { 3 / 2 }$

Determine algebraically whether the following function is one-to-one. $f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$ , where $x > 0$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Find $f \circ g$ $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Calculus Practice Problems

Filters

Exam 1: Functions and Their Graphs

Use the functions f(x)=1125x−5f ( x ) = \frac { 1 } { 125 } x - 5f(x)=1251​x−5 and g(x)=x3g ( x ) = x ^ { 3 }g(x)=x3 to find (f∘g)−1( f \circ g ) ^ { - 1 }(f∘g)−1 .

Use function notation to write ggg in terms of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ . g(x)=−13x−8+7g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7g(x)=−31​x−8​+7

Find f∘gf \circ gf∘g . f(x)=3x−2g(x)=x−5f ( x ) = 3 x - 2 \quad g ( x ) = x - 5f(x)=3x−2g(x)=x−5

Determine the domain and range of the inverse function f−1f ^ { - 1 }f−1 of the following function fff f(x)=−∣x+6∣+2f ( x ) = - | x + 6 | + 2f(x)=−∣x+6∣+2 , where x>−6x > - 6x>−6

Determine the domain of g(x)=1x2−81g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }g(x)=x2−811​ .

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=−2x+55f ( x ) = \frac { - 2 x + 5 } { 5 }f(x)=5−2x+5​

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (−4,7)( - 4,7 ) \quad(−4,7) line: −5x−15y=−6- 5 x - 15 y = - 6−5x−15y=−6

Evaluate the following function at the specified value of the independent variable and simplify. f(u)=4u2+12u2;f(0)f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )f(u)=u24u2+12​;f(0)

Find the inverse function of fff . f(x)=x9−2f ( x ) = x ^ { 9 } - 2f(x)=x9−2

Determine whether lines L1L _ { 1 }L1​ and L2L _ { 2 }L2​ passing through the pairs of points are parallel, perpendicular, or neither. :(7,-4),(-9,-1) :(4,-6),(-3,9)

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−15(x+4)3g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }g(x)=−51​(x+4)3

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=49x2−64f ( x ) = 49 x ^ { 2 } - 64f(x)=49x2−64

Find f∘gf \circ gf∘g . f(x)=−4x+3g(x)=x+7f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7f(x)=−4x+3g(x)=x+7

Algebraically determine whether the function below is even, odd, or neither. f(q)=2q3/2f ( q ) = 2 q ^ { 3 / 2 }f(q)=2q3/2

Determine algebraically whether the following function is one-to-one. f(x)=5x23x2+6f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }f(x)=3x2+65x2​ , where x>0x > 0x>0

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−12(x+9)3g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }g(x)=−21​(x+9)3

Find the slope-intercept form of the line passing through the points. (−1,−6),(0,−2)( - 1 , - 6 ) , ( 0 , - 2 )(−1,−6),(0,−2)

Find f∘gf \circ gf∘g f(x)=x+3g(x)=4x2−9f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }f(x)=x+3g(x)=x2−94​

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Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Find $f \circ g$ . $f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 6 | + 2$ , where $x > - 6$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { - 2 x + 5 } { 5 }$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 ) \quad$ line: $- 5 x - 15 y = - 6$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$

Find the inverse function of $f$ . $f ( x ) = x ^ { 9 } - 2$

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither. :(7,-4),(-9,-1) :(4,-6),(-3,9)

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Find $f \circ g$ . $f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

Algebraically determine whether the function below is even, odd, or neither. $f ( q ) = 2 q ^ { 3 / 2 }$

Determine algebraically whether the following function is one-to-one. $f ( x ) = \frac { 5 x ^ { 2 } } { 3 x ^ { 2 } + 6 }$ , where $x > 0$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Find $f \circ g$ $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$