Answer
(a) $f(x)$ is even function.
(b) $g(x)$ is neither even nor odd.
(c) $f(x)$ is even.
Work Step by Step
(a) $f(x)=x^4-3x^2$, since $$f(-x)=(-x)^4-3(-x)^2=x^4-3x^2=f(x)$$
then $f(x)$ is an even function.
(b) $g(x)=\sin(x+1)$, since $g(-x)=\sin(-x+1)\neq g(x)$ and $g(-x)\neq -g(x)$, then $g(x)$ is neither even nor odd.
(c) since $f(-x)=2^{-(-x)^2}=2^{-x^2}=f(x)$ then $f(x)$ is even.
