Question

Find f if g(x)=9x+(3/x) and (fog)(x)=81x^2+(9/x^2)

Answer 1

fog(x) as in fg(x) ?

Answer 2

\[f(x) = x^2 -54\]
If you want to know how to get it, make question.

Answer 3

Is it the same form used in defining chain rule?
F(x)=(f o g)(x),
F'(x)=f'(g(x))*g'(x).
I think this problem needs linear algebra, which however I almost forget.
There probably more than one answer.

Answer 4

But the above guy is actually right, the simple observation gives at least one answer, R(x)=81x^2+(9/x^2)=f(g(x))=g(x)^2-54,
so f(x)=x^2-54 is one answer.