Answer:
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
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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.
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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.
