Answer
(a) odd function.
(b) odd function.
(c) neither odd nor even function.
(d) even function.
Work Step by Step
(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.
