Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y=9/sqrt(5x+5)

Answer 1

Remember first that y=f(g(x)) means: put a number in g, then punt the result in f.
To see what the functions you are looking for could be, try substituting some number for x and calculate y yourself, e.g.: what if I set x = 2?

Well, I would have to to multiply it by 5, than add 5, then take the square root, then divide 9 by this last outcome. That's FOUR steps instead of two...
Now, could we do some of the steps together in one function?
Sure, g(x) = 5x+5 is one neat little linear function.
Can you see function f? (remember what f has to do with a number is: take the square root, then divide 9 by this root...)

Answer 2

You will have found:\[f(x)=\frac{ 9 }{ \sqrt{x} }\]