Chapter 3.2, Problem 7E

Show that each of the following functions $f:A\to H$ is one-to-one. Find the range of each function and a suitable inverse.

1. $A=\left\{x\in R|x\ne 4\right\},f\left(x\right)=1+\frac{1}{x-4}$

2. $A=\left\{x\in R|x\ne -1\right\},f\left(x\right)=5-\frac{1}{1+x}$

3. $A=\left\{x\in R|x\ne -\frac{3}{2}\right\},f\left(x\right)=\frac{3x}{2x+1}$

4. $A=\left\{x\in R|x\ne -3\right\},f\left(x\right)=\frac{x-3}{x+3}$