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Function Inverse - Function to Inverse (Exponential/Logarithmic)

Level 1

This math topic focuses on finding the inverse functions of exponential and logarithmic functions. The problems require converting given exponential or logarithmic functions into their inverse forms. Each example features a function, such as a logarithmic function with a base or a natural logarithm (`ln`), and the task is to determine the correct inverse function from multiple choices. This is a fundamental exercise in understanding how functions and their inverses work, particularly within the realms of exponential and logarithmic operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Inverse - Function to Inverse (Exponential/Logarithmic) Worksheet

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Function Inverse - Function to Inverse (Exponential/Logarithmic)
1
A LaTex expression showing \begin{align*}\text{given:}&\\m(x) &= 2\log{(4 x)}\\m to the power of -1 (x) &= ?\end{align*}
Find the inverse function of m(x)
a A LaTex expression showing m to the power of -1 (x) = 4\frac{10 to the power of x }{2}
b A LaTex expression showing m to the power of -1 (x) = 10 to the power of \frac{x over 2 }{4}
2
A LaTex expression showing \begin{align*}\text{given:}&\\c(x) &= 3 times -2 to the power of -5 x \\c to the power of -1 (x) &= ?\end{align*}
Find the inverse function of c(x)
a A LaTex expression showing c to the power of -1 (x) = \log sub - 2{ \frac{x over 3 }}{-5}
b A LaTex expression showing c to the power of -1 (x) = \log sub - 2{ \frac{x over -5 }}{3}
3
A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= 3\log sub 2 {(-4 x)}\\z to the power of -1 (x) &= ?\end{align*}
Find the inverse function of z(x)
a A LaTex expression showing z to the power of -1 (x) = 2 to the power of \frac{x over 3 }{-4}
b A LaTex expression showing z to the power of -1 (x) = 2 to the power of \frac{x over -4 }{3}
4
A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= 4\log sub 3 {(2 x)}\\y to the power of -1 (x) &= ?\end{align*}
Find the inverse function of y(x)
a A LaTex expression showing y to the power of -1 (x) = 3 to the power of \frac{x over 2 }{4}
b A LaTex expression showing y to the power of -1 (x) = 3 to the power of \frac{x over 4 }{2}
5
A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= -4\log sub 5 {(-2 x)}\\z to the power of -1 (x) &= ?\end{align*}
Find the inverse function of z(x)
a A LaTex expression showing z to the power of -1 (x) = 5 to the power of \frac{x over -2 }{-4}
b A LaTex expression showing z to the power of -1 (x) = 5 to the power of \frac{x over -4 }{-2}
6
A LaTex expression showing \begin{align*}\text{given:}&\\n(x) &= -3\log sub 5 {(4 x)}\\n to the power of -1 (x) &= ?\end{align*}
Find the inverse function of n(x)
a A LaTex expression showing n to the power of -1 (x) = 5 to the power of \frac{x over 4 }{-3}
b A LaTex expression showing n to the power of -1 (x) = 5 to the power of \frac{x over -3 }{4}
7
A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 5 to the power of 3 x \\p to the power of -1 (x) &= ?\end{align*}
Find the inverse function of p(x)
a A LaTex expression showing p to the power of -1 (x) = \frac{\log sub 5 {x}}{3}
b A LaTex expression showing p to the power of -1 (x) = \frac{\log sub 5 {3}}{x}
8
A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 5\ln{(2 x)}\\p to the power of -1 (x) &= ?\end{align*}
Find the inverse function of p(x)
a A LaTex expression showing p to the power of -1 (x) = e to the power of \frac{x over 5 }{2}
b A LaTex expression showing p to the power of -1 (x) = e to the power of \frac{x over 2 }{2}