Chapter 1, Problem 38RE

In each part, find $f^{-1}\left(x\right)$ if the inverse exists.

(a) $f\left(x\right)={\left(e^x\right)}^2+1$

(b) $f\left(x\right)=\sin \left(\frac{1-2x}{x}\right),\frac{2}{4+\pi }\le x\le \frac{2}{4-\pi }$

(c) $f\left(x\right)=\frac{1}{1+3{\tan }^{-1}x}$