Inverse Functions · Review Exercise 123

For the following exercise, find a domain on which the function $f$ is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of $f$ restricted to that domain.

Given $f\left(x\right)=x^3-5$ and $g\left(x\right)=\sqrt[3]{x+5}:$

(a) Find $f\left(g\left(x\right)\right)$ and $g\left(f\left(x\right)\right).$
(b) What does the answer tell us about the relationship between $f\left(x\right)$ and $g\left(x\right)?$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Precalculus 2e · §1.7 Inverse Functions · Review Exercise 123