systems of equations involving composition of functions

45 Views Asked by At

If we are given a function

$g(x) = x - 1/x$

And another one given in terms of composition

$f(g(x)) = x^3 - 1/x^3$

By which general method does one find $f(x)$ ?

Can it be found for arbitrary $g(x)$ and $f(g(x)$?