# Thread: I have tried this problem 8 times, I need some help!

1. ## I have tried this problem 8 times, I need some help!

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).

2. Originally Posted by md56
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 $\displaystyle x$.

3. So f(g(x)) is equal to 1/(x+9)?

4. Originally Posted by md56
So f(g(x)) is equal to 1/(x+9)?
Yeah.

Remember, you have h(x), and you're trying to express h(x) in terms of f(g(x)).

So we're spitting one function, h(x), into a function of a function f(g(x)).

So the first fact we deal with in this problem is that:

h(x) = f(g(x))

and we are told that h(x) = 1/(x+9).