Find $f(x) + g(x)$, $f(x) - g(x)$, $f(x) \cdot g(x)$, $\frac{f(x)}{g(x)}$, $f(g(x))$, and $g(f(x))$, If defined. (If an answer is undefined, enter UNDEFINED.)
$f(x) = \frac{x}{x+9}$
$g(x) = x^7$
(a) $f(x) + g(x)$
(b) $f(x) - g(x)$
(c) $f(x) \cdot g(x)$
(d) $\frac{f(x)}{g(x)}$
(e) $f(g(x))$
(f) $g(f(x))$