inverse composition function help please

[mcnscott]

I'm trying to solve this homework exercise but I'm totally lost on it.

assume f, g, h are invertible functions and that f(x) = g(h(x)). Find a formula for f^-1 in terms of g^-1 AND h^-1

I've written this problem out several ways but none of it makes sense i've tried to substitute fake values for the functions but with no luck.

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

h(x) = the input for g

without some numbers to substitute that I know work to make the function true I'm very stumped.

 

[Gene]

f^-1(x) = h^-1(g^-1(x)).
Try it out with
g(x)=x^2
g^-1(x)=sqrt(x)
h(x)=x^2
h^-1(x)=x/2