### Home > INT3 > Chapter 7 > Lesson 7.2.3 > Problem7-86

7-86.
1. What is the inverse function of each of the following functions? Use any method to write an equation for the inverse function. Be sure to restrict domains as necessary. 7-86 HW eTool (Desmos) Desmos Accessibility Homework Help ✎

1. f(x) = x2 + 3

2. f(x) =

3. f(x) =

Use the eTool below to graph the function and its inverse.
Click the link at right for the full version of the eTool: Draw Inverse eTool
Domain restrictions can be added to a function by using brackets, for example {x > 1}. Make sure both of the graphs are functions.

This function squares the input then adds 3. How can this be undone? Use the eTool to check your answer.

Let f(x) = y. Interchange x and y. Solve for y in the new equation.

$x = \left( \frac{1}{4}y+6\right)^3$

$\sqrt[3]{x}=\frac{1}{4}y+6$

$\sqrt[3]{x}-6=\frac{1}{4}y$

$f^{-1} = 4(\sqrt[3]{x}-6)$

To undo square rooting, square both sides of the equation.

$f^{-1}(x)=\frac{x^2+6}{5}$