Suppose $\displaystyle f(x) = \frac{g(x)}{h(x)}$, where $g(x) = 3x^{3}+x$ and $h(x) = x^{5}-8x^{3}$.

(a) Find $f(-x)$ by simplifying $g(-x)$ and $h(-x)$ as much as possible and entering them in the numerator and denominator below.

$\displaystyle f(-x) =$

(b) Reduce the fraction in part (a) further by factoring and cancellation, if possible. Then for all $x$, $f(-x) =$
A. $f(x)$
B. $-f(x)$
C. None of the above

(c) Is $f$ an even function, an odd function, or neither even nor odd?
A. Even
B. Odd
C. Neither