Chapter 7, Problem 5AAE

(a)

To determine

Prove that $g\left(x\right)+h\left(x\right)=0$ for all x, then $g\left(x\right)=0$ for all x and $h\left(x\right)=0$ for all x.

(b)

To determine

Prove that if $f\left(x\right)=f_E\left(x\right)+f_O\left(x\right)$ is the sum of an even function $f_E\left(x\right)$ and an odd function $f_O\left(x\right)$ by using part (a).

(c)

To determine

Provide the significant of the result in part (b).