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

Answer:

Step-by-step 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