## Calculus (3rd Edition)

(a) Since we have $f(-t)=\frac{1}{t^4-t+1}-\frac{1}{t^4+t+1}=-f(t)$, then $f$ is an odd function. (b) Since we have $g(-t)=2^{-t}-2^t=-f(t)$, then $f$ is an odd function. (c) Since we have $f(-\theta)=-\sin\theta+\cos\theta\neq f(\theta)\neq -f(\theta)$, then $f$ is neither an odd nor even function. (d) Since we have $H(-\theta)=\sin\theta^2= H(\theta)$, then $H$ is an even function.