Will mark find f(x) and g(x) so that the function can be described as y = f(g( y = 8/x^2 + 2

One possibility is ...

... f(x) = 2/x +2

... g(x) = (x/2)^2

Step-by-step explanation:

There are very many possibilities. The only requirement is that when you put the expression for g(x) in the place of x in the definition of f(x), the result simplifies to ...

... f(g(x)) = 2/x^2 +2

For the suggested functions, we have

... f((x/2)^2) = 2/(x/2)^2 +2 = 2·4/x^2 +2 = 8/x^2 +2 . . . . as desired.

Alternate Solutions

One of the simplest might be ...

... g(x) = x

... f(x) = 8/x^2 +2

Then f(g(x)) = f(x) = 8/x^2 +2.

d

gimmee one of those gold crowns!

~coco