Answer
(a) even
(b) neither
(c) odd
Work Step by Step
Use $f(-x)$ to test each function, we have:
(a) $f(-x)=(-x)^2-7=x^2-7=f(x)$, thus it is an even function.
(b) $f(-x)=(-x)^3-(-x)-1=-x^3+x-1$, as $f(-x)\ne f(x)$ and $f(-x)\ne -f(x)$, it is neither even nor odd.
(c) $f(-x)=(-x)^{101}-(-x)^{99}=-x^{101}+x^{99}=-f(x)$, thus it is an odd function.