Answer
a. odd b. odd c. odd d. even e. even f. even g. even h. even i. odd
Work Step by Step
Given $ f(-x)=f(x)$ and $ g(-x)=-g(x)$, we have
a. $ f(-x)g(-x)=-f(x)g(x)$: odd function
b. $\frac{f(-x)}{g(-x)}=-\frac{f(x)}{g(x)}$: odd function
c. $\frac{g(-x)}{f(-x)}=-\frac{g(x)}{f(x)}$: odd function
d. $ f(-x)f(-x)=f(x)f(x)$: even function
e. $ g(-x)g(-x)=g(x)g(x)$: even function
f. $ f(g(-x))=f(-g(x))=f(g(x))$: even function
g. $ g(f(-x))=g(f(x))$: even function
h. $ f(f(-x))=f(f(x))$: even function
i. $ g(g(-x))=g(-g(x))=-g(g(x))$: odd function
