Textbook Problem

a. Show that the mapping $f$ given in Example 2 is neither onto nor one-to-one.

b. For this mapping $f$, show that if $S=\left\{1,2\right\}$, then $f^{-1}\left(f\left(S\right)\right)\ne S$.

c. For this same $f$ and $T=\left\{4,9\right\}$, show that $f\left(f^{-1}\left(T\right)\right)\ne T$.