Inverse Functions · Exercise 21

Find a domain on which each 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 $f\left(x\right)=\frac{x}{2+x}$ and $g\left(x\right)=\frac{2x}{1-x}:$

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

OpenStax, Algebra and Trigonometry 2e · §3.7 Inverse Functions · Exercise 21