determine the three functions that made this answer... f(x),g(x),h(x)?

I think that there could be more than one solution.

But what comes to my mind immediately is:

f(g(h(x))) = sin^2(x+1)

f(x+1) = sin^2(x+1)

So,

f(x) = sin^2(x)

and g(h(x)) = x+1

Then, g(x) = x+1

which means that h(x) = x

thanks but I got the answer it is
h(x)= x+1
g(x)= sin (x)
f(x)= x^(2)

Yes, this too is a solution. As I told you, there can be many different solutions if no more information is given.

You can try working with what I came up with and you'll get the same thing :)