Function Inverse - Function to Inverse (Level 1)

Level 1

This math topic focuses on finding the inverse of given functions. It covers various types of functions, including linear, quadratic, and rational expressions. The problems are structured to help understand the relationship between functions and their inverses by calculating the inverse for specific mathematical expressions. Each question provides two potential answers in a multiple-choice format, challenging the understanding and application of the concept of function inversion. This is a fundamental aspect of understanding functions, composition, and inversion in intro-level math courses.

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

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Function Inverse - Function to Inverse Worksheet

Function Inverse - Function to Inverse

$A LaTex expression showing \begin{align*}\text{given:}&\\n(x) &= 2 over 3x \\n to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of n(x)

A LaTex expression showing n to the power of -1 (x) = 2 over 3x

A LaTex expression showing n to the power of -1 (x) = 6 over x

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 4square root of 5x\\p to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of p(x)

A LaTex expression showing p to the power of -1 (x) = 20 over x to the power of 2

A LaTex expression showing p to the power of -1 (x) = x to the power of 2 over 80

$A LaTex expression showing \begin{align*}\text{given:}&\\d(x) &= -3 x+2\\d to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of d(x)

A LaTex expression showing d to the power of -1 (x) = x-2 over -3

A LaTex expression showing d to the power of -1 (x) = -3-2 over x

$A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= 5 x to the power of 2 \\z to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of z(x)

A LaTex expression showing z to the power of -1 (x) = -square root of x over 5

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 2 x-3\\p to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of p(x)

A LaTex expression showing p to the power of -1 (x) = x-3 over 2

$A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= 4 x+5 over -2 \\y to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of y(x)

A LaTex expression showing y to the power of -1 (x) = -2 x-5 over 4

A LaTex expression showing y to the power of -1 (x) = 4 ({-2 x-5)

$A LaTex expression showing \begin{align*}\text{given:}&\\r(x) &= -3 x to the power of 2 \\r to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of r(x)

A LaTex expression showing r to the power of -1 (x) = -square root of x over -3

$A LaTex expression showing \begin{align*}\text{given:}&\\d(x) &= 4 over -3x \\d to the power of -1 (x) &= ?\end{align*}$

Find the inverse function of d(x)

A LaTex expression showing d to the power of -1 (x) = 4x over -3

A LaTex expression showing d to the power of -1 (x) = 4 over -3x