## Calculus (3rd Edition)

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).