Textbook Problem

For each of the following mappings, write out $f\left(S\right)$ and $f^{-1}\left(T\right)$ for the given $S$ and $T$, where $f:Z\to Z$.

a. $f\left(x\right)=\left|x\right|;S=Z-E,T=\left\{1,3,4\right\}$

b. $f\left(x\right)=\{\begin{array}{cc}x+1& \text{if }x\text{is even}\\ x& \text{if }x\text{is odd;}\end{array}S=\left\{0,1,5,9\right\}T=Z-E$

c. $f\left(x\right)=x^2;S=\left\{-2,-1,0,1,2\right\},T=\left\{2,7,11\right\}$

d. $f\left(x\right)=\left|x\right|-x;S=T=\left\{-7,-1,0,2,4\right\}$.