Solutions

a) $y$.

b) $H(y)$.

c) $H(y)$.

d) Let $H$ be a function having the points defined in the problem. If we limit the domain of $H$ to those points, then the property $H(H(x))=H(x)$ for all $x$ is satisfied.

e) Let $H$ be a function having the points in the problem and add $(7,7)$ and $(18,18)$ to it. Thus, $H$ is defined as

$$H=\{(1,7),(7,7),(17,18),(18,18)\}$$

and satisfies $H(H(x))=H(x)$ for all $x$.