Exam 4: Inverse, Exponential, and Logarithmic Functions

Solve the problem. -Suppose that the salinity $\mathrm { S }$ of ocean water at a given depth $\mathrm { d }$ is modeled by the equation $\mathrm { S } ( \mathrm { d } ) = 29.9 + 1.4 \log ( \mathrm { d } + 1 )$ , where $\mathrm { S }$ is measured in grams salt per kilogram water and $\mathrm { d }$ is measured in meters. What is the salinity when the depth is $998 \mathrm {~m}$ ? Round your answer to the nearest hundredth.

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f(x)=x^{2}-4$

Provide an appropriate response. -Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $\left( 2 , \frac { 1 } { 49 } \right)$ . Assume that $a > 0$ .

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = - \sqrt { x ^ { 2 } - 25 } , x \geq 5$

Determine the function value. -Suppose $f ( x ) = \log _ { a } ( x )$ and $f ( 11 ) = 2$ . Find $f \left( \frac { \sqrt { 11 } } { 11 } \right)$

Solve the equation. - $\log _ { 2 } \frac { 1 } { 16 } = x$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ . Find $f \left( \frac { 5 } { 2 } \right)$ .

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 5 ; [ - 3,3 ] \text { by } [ - 40,40 ]$

Find the future value. -$1517 invested for 9 years at 6% compounded quarterly

Decide whether the given functions are inverses. - =\{(-2,-5),(1,5),(5,-2),(7,11)\} =\{(-5,-2),(5,1),(-2,5),(11,7)\}

Write the word or phrase that best completes each statement or answers the question. -Given $f ( x ) = \log _ { 4 } x$ , evaluate the following. (a) $\mathrm { f } \left( 4 ^ { 4 } \right)$ (b) $f \left( 4 ^ { \log _ { 4 } 4 } \right)$ (c) $f \left( 44 \log _ { 4 } 4 \right)$

Find the value. Give an approximation to four decimal places. - $\ln \left( \frac { 83 } { 28 } \right)$

Solve the problem. -At what interest rate must $5400 be compounded annually to equal $7930.08 after 13 yr? (Round to the nearest percent.)

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $f ( x ) = x ^ { 3 } - 8$

Solve the equation and express the solution in exact form. - $\ln x - \ln ( x - 5 ) = \ln 9$

Write in logarithmic form. - $2 ^ { - 3 } = \frac { 1 } { 8 }$

If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ - $\{ ( 6 , - 7 ) , ( 11 , - 6 ) , ( 9 , - 5 ) , ( 7 , - 4 ) \}$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt { x - 2 }$

Solve the problem. -Let f(x) compute the time in hours to travel x miles at 25 miles per hour. What does f-1(x) compute?

Graph the function. Give the domain and range. - $f(x)=\log _{3}(x+3)$