Chapter 9.5, Problem 52E

To determine

To find: the inverse function.

Answer to Problem 52E

The inverse function is $f^{-1}\left(x\right)=\sqrt[3]{7-x}$ .

Explanation of Solution

Given information:

Thefunction is $f\left(x\right)=7-x^3$

Calculation: to find the inverse function, first substitute $y=f\left(x\right)$ and then simplify,

  $\begin{array}{l}f\left(x\right)=7-x^3\\ y=7-x^3\text{ [substitute]}\\ x^3=7-y\text{ [subtract]}\\ x=\sqrt[3]{7-y}\text{ [cube root]}\\ f^{-1}\left(x\right)=\sqrt[3]{7-x}\end{array}$

Thus, The inverse function is $f^{-1}\left(x\right)=\sqrt[3]{7-x}$ .