Question

If anyone can give an explanation with how to do this it would be nice, the modules on this homework application aren't cutting it for me.

Answer 1

Explanation:

The given H(x) = √(2 - 2x^2) can be decomposed as follows: 2 - 2x^2 is g(x), the input to f(x), which in turn is f(x) = √x.

Thus, f(x) = √x is the first function. Here the input is simply x.

g(x) = 2 - 2x^2 is the second function. We use this function now as the input to f(x). These operations create the new function H(x) = (f°g)(x) = √(2 - 2x^2).

In summary:

f(x) = √x

g(x) = 2 - 2x^2