## Calculus (3rd Edition)

(a) $f(x)$ is even function. (b) $g(x)$ is neither even nor odd. (c) $f(x)$ is even.
(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.