Express the function h(x)=1/x+9 in the form f of g. If g(x) equals x+9, find the function f(x).
I assume you mean $\displaystyle h(x) = \frac{1}{x+9} $, rather than $\displaystyle h(x) = \frac{1}{x} + 9 $, but correct me if I am wrong.
Well we know that $\displaystyle g(x) = x+9 $, and we know that $\displaystyle f(g(x)) = h(x) $
Which means:
$\displaystyle f(g(x)) = \frac{1}{x+9} $
$\displaystyle \therefore f(g(x)) = \frac{1}{g(x)} $
You can find out what $\displaystyle f(x) $ is from here by replacing $\displaystyle g(x) $ with $\displaystyle x$.