Exam 4: Inverse, Exponential, and Logarithmic Functions

Use a graphing utility to graph the functions given by ​ $y _ { 1 } = \ln ( x ) - \ln ( x - 4 )$ ​ and ​ $y _ { 2 } = \ln \frac { x } { x - 4 }$ ​ in the same viewing window. ​

Find the inverse function of $f ( x ) = \sqrt { 25 - x ^ { 2 } } , 0 \leq x \leq 5$ . ​

Select the graph of the function. ​ $f ( x ) = \log ( x + 4 )$ ​

Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 2 }$ .

Determine whether the function has an inverse function. If it does, find the inverse function. ​ $f ( x ) = - 3$ ​

Approximate the point of intersection of the graphs of f and g. Then solve the equation $f ( x ) = g ( x )$ algebraically to verify your approximation. ​ f(x)= g(x)=9 ​ ​

Select the graph of the function. ​ $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { - x }$ ​

Match the graph with its exponential function. ​ ​

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms. Then use a graphing utility to graph the ratio. ​ $f ( x ) = \log _ { 4 } ( x )$ ​

Use a graphing utility to construct a table of values for the function. Round your answer to two decimal places. ​ $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ ​

Evaluate the function at the indicated value of x. Round your result to three decimal places. ​ Function Value $f ( x ) = 3 ^ { x }$ $x = - \pi$ ​

Your wage is $11.00 per hour plus $1.25 for each unit produced per hour. So, your hourly wage in terms of the number of units produced x is $y = 11 + 1.25 x$ . Find the inverse function. What does each variable represent in the inverse function? ​

Use the functions given by $f ( x ) = \frac { 1 } { 27 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ . ​

Use a graphing utility to construct a table of values for the function. Round your answer to three decimal places. ​ $f ( x ) = 6 e ^ { x - 2 } + 7$ ​

Solve for x. ​ $\log x = - 1$ ​