Chapter 1.2, Problem 17E

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

a. For $S=\left\{0,1,2\right\},$ find $f\left(S\right)$ and $f^{-1}\left(f\left(S\right)\right)$.

b. For $T=\left\{-1,1,4\right\},$ find $f^{-1}\left(T\right)$ and $f\left(f^{-1}\left(T\right)\right)$.

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