Chapter 3.2, Problem 2E

(a)Show that the function $h:\mathbb{Z}\to \mathbb{Z}$ defined by $h\left(x\right)=3x$ is not a ring homomorphism.
(b)Show that the function $h:{\mathbb{Z}}_6\to {\mathbb{Z}}_6$ defined by $h\left(x\right)=2x$ is not a ring homomorphism.
(c)Let $\mathbb{Z}\left[x\right]$ be the set of all polynomials $p\left(x\right)$ in the variable x with integer coefficients. Show that the function $g:\mathbb{Z}\left[x\right]\to \mathbb{Z}$ defined by $g\left(p\left(x\right)\right)=p\left(0\right)$ is a ring homomorphism.