Answer
a. neither even nor odd.
b. odd
c. even
d. neither even nor odd.
Work Step by Step
a.
$f(-x)=2(-x)^{5}-3(-x)^{2}+2$
$=-2x^{5}-3x^{2}+2$,
which is neither $f(x)$ nor $-f(x)$, so the function is neither even nor odd.
b,
$f(-x)=(-x)^{3}-(-x)^{7}=-x^{3}+x^{7}=-f(x).$
Odd.
c.
$f(-x)=\cos((-x)^{2})=\cos(x^{2})=f(x)$
Even.
d.
$f(-x)=1+\sin(-x)=1-\sin x,$
neither even nor odd.
