Chapter 1.2, Problem 16E

Let $g:Z\to Z$ be given by $g\left(x\right)=\{\begin{array}{cc}x& \text{if }x\text{is even}\\ \frac{x+1}{2}& \text{if }x\text{is odd}\text{.}\end{array}$

a. For $S=\left\{3,4\right\}$, find $g(S)$ and $g^{-1}(g(S))$.

b. For $T=\left\{5,6\right\},$ find $g^{-1}\left(T\right)$ and $g\left(g^{-1}\left(T\right)\right)$.