3.7 Exercise 42

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 $g \left(x\right) = \frac{2 x}{1 - x} :$

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