Thread: 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).

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 , rather than , but correct me if I am wrong.

Well we know that , and we know that

Which means:





You can find out what is from here by replacing with .

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

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).