express function in form f o g o h (use non identity functions for fgh)

Question

H(x) = 3-4^x^2

Answer 1

Let h() = x², g(x) = 4^x, and f(x) = 3 - x

Then, (f o g o h)(x) = f(g(h(x)) = f(g(x²)) = f(4^{x^2}) = 3 - 4^{x^2} = H(x)