Question 1

Let T(x) = 2x 2  - 3x. Find (and simplify) the expression. T (x + 3) - T (x - 3)

Accepted Answer

A)  24x 
B)  18x - 24 
C)  24x - 18 
D)  6x 
E)  18x 
A)  24x 
B)  18x - 24 
C)  24x - 18 
D)  6x 
E)  18x

Question 2

Let f(x) = x 3  + 2x + 1, and assume that the domain of f -1  is $( - \infty , \infty )$ . Simplify $f \left[ f ^ { - 1 } ( t + 5 ) \right]$ .

Accepted Answer

A)  t 3  + 3t + 5 
B)  (t + 5)  2  
C)  $\frac { 1 } { t + 5 }$ 
D)  t 2  + 2t + 1 
E)  t + 5 
A)  t 3  + 3t + 5 
B)  (t + 5)  2  
C)  $\frac { 1 } { t + 5 }$ 
D)  t 2  + 2t + 1 
E)  t + 5

Question 3

Determine the domain and the range. $g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }$

Accepted Answer

A)  domain: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$ range: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; 
B)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 20 } { 11 } \right) \cup \left( \frac { 20 } { 11 } , \infty \right)$ 
C)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$ 
D)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 3 } { 11 } \right) \cup \left( \frac { 3 } { 11 } , \infty \right)$ 
E)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 18 } \right) \cup \left( \frac { 11 } { 18 } , \infty \right)$ 
A)  domain: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$ range: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; 
B)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 20 } { 11 } \right) \cup \left( \frac { 20 } { 11 } , \infty \right)$ 
C)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 3 } \right) \cup \left( \frac { 11 } { 3 } , \infty \right)$ 
D)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 3 } { 11 } \right) \cup \left( \frac { 3 } { 11 } , \infty \right)$ 
E)  domain: $( - \infty , 6 ) \cup ( 6 , \infty )$ ; range: $\left( - \infty , \frac { 11 } { 18 } \right) \cup \left( \frac { 11 } { 18 } , \infty \right)$

Question 4

Let f(x) = 5x + 4. Find f - 1 (x).

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 5 } { 4 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 4 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 8 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 5 } - 4$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { 5 x - 4 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x + 5 } { 4 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 4 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 8 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 5 } - 4$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { 5 x - 4 }$

Let T(x) = 2x² - 3x. Find (and simplify) the expression. T (x + 3) - T (x - 3)

Let f(x) = x³ + 2x + 1, and assume that the domain of f^-1 is $( - \infty , \infty )$ . Simplify $f \left[ f ^ { - 1 } ( t + 5 ) \right]$ .

Determine the domain and the range. $g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }$

Let f(x) = 5x + 4. Find f^{- 1}(x).

Fundamentals

Equations and Inequalities

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 3: Functions

Let T(x) = 2x 2 - 3x. Find (and simplify) the expression. T (x + 3) - T (x - 3)

Let f(x) = x 3 + 2x + 1, and assume that the domain of f -1 is (−∞,∞)( - \infty , \infty )(−∞,∞) . Simplify f[f−1(t+5)]f \left[ f ^ { - 1 } ( t + 5 ) \right]f[f−1(t+5)] .

Determine the domain and the range. g(x)=11x−203x−18g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }g(x)=3x−1811x−20​

Let f(x) = 5x + 4. Find f - 1 (x).

Fundamentals

Equations and Inequalities

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Let T(x) = 2x² - 3x. Find (and simplify) the expression. T (x + 3) - T (x - 3)

Let f(x) = x³ + 2x + 1, and assume that the domain of f^-1 is $( - \infty , \infty )$ . Simplify $f \left[ f ^ { - 1 } ( t + 5 ) \right]$ .

Determine the domain and the range. $g ( x ) = \frac { 11 x - 20 } { 3 x - 18 }$

Let f(x) = 5x + 4. Find f^{- 1}(x).