Answer
a) odd
b) neither odd nor even
c) even
Work Step by Step
a) $f(x)= x^{5}$
$f(-x)= (-x)^{5}=-x^{5}= -f(x)$.
A function is odd when $f(-x)=-f(x)$ for all x. Therefore, this is an odd function.
b) $g(t)= t^{3}-t^{2}$
$g(-t)= (-t)^{3}-(-t)^{2}= -t^{3}-t^{2}\ne g(t)$
Also, $g(-t)\ne -g(t)$. Therefore, this function is neither odd nor even.
c) $F(t)=\frac{1}{t^{4}+t^{2}}$
$F(-t)= \frac{1}{(-t)^{4}+(-t)^{2}}=\frac{1}{t^{4}+t^{2}}= F(t)$
F is even as F(-t)=F(t).
