Question

Hi! I really need help with this. I'm so confused. Thanks! :)


If h(x)=4/(5x+2)^2, find the two functions f and g so that f(g(x))=h(x).

Answer 1

you have to learn to recognize the patterns.

It looks like the primary function is 4/(something)^2
so let f(x) = 4/x^2

Now I see that instead of x in the denominator , I see 5x+2
so I let g(x) = 5x+2

so f(x) = 4/x^2 and g(x) = 5x+2

check:
suppose we find f(g(x))
= f(5x+2)
= 4/(5x+2)^2
= h(x)