Exam 5: Inverse, Exponential, and Logarithmic Functions

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm { f } ^ { - 1 } ( 3 )$

Solve for the indicated variable. - $\log _ { c } ( z + y ) = \log _ { c } ( 2 z - 4 )$ , for $y$

Match the function with its graph. - $f ( x ) = \log _ { 4 } \left( \frac { x } { 4 } \right)$

Solve for the indicated variable. - $\mathrm { D } = \mathrm { D } _ { 0 } \mathrm { e } ^ { \mathrm { kt } / 800 , }$ , for $\mathrm { t }$

Solve the equation and express the solution in exact form. - $\ln x - \ln ( x - 4 ) = \ln 9$

Write in logarithmic form. - $2 ^ { - 2 } = \frac { 1 } { 4 }$

Choose the one alternative that best completes the statement or answers the question. -In the formula N $\mathrm { N } = \mathrm { Ie } ^ { \mathrm { kt } }$ N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for The population of a certain country to triple if its annual growth rate is 7.5%? Round to the nearest Year.

Solve the equation. - $2 ( 8 - 2 x ) = 4$

Determine whether or not the function is one-to-one. - $f ( x ) = \left| 64 - x ^ { 2 } \right|$

Graph the function. Give the domain and range. - $\mathrm{f}(\mathrm{x})=\left|\log _{1 / 2}(\mathrm{x}+2)\right|$

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

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 7 x - 4$

Solve the equation and express the solution in exact form. - $\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$

Choose the one alternative that best completes the statement or answers the question. -In the formula N $\mathrm { N } = \mathrm { Ie } ^{\mathrm { kt }}$ , N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 69 Million cars in a certain country, decreasing by 6.3% annually. How many years will it take for this Country to have 51 million cars? Round to the nearest year.

Decide whether the given functions are inverses. - x f(x) 3 12 4 18 5 24 6 30 7 36 x g(x) 12 3 18 4 24 5 30 6 36 7

Decide whether the pair of functions graphed are inverses. -

Solve the equation. Round to the nearest thousandth. - $2 ( x - 1 ) = 10$

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of $h ( x ) = a ^ { - x }$ . Give the domain and range of $h$ . $f(x)=a^{x}$

Determine whether the statement is true or false. -If a function f has an inverse function, then f is one-to-one.

Evaluate the logarithm. - $\log _ { 6 } \sqrt { 6 }$