Question

Suppose \(f(x)\) is a rational function such that
\(3 f \left( \frac{1}{x} \right) + \frac{2f(x)}{x} = x^2\)
for all \(x \neq 0\). Find \(f(-2)\).

Answer 1

I wonder if you get a system of equations by entering in -2 and also -1/2 you know separately.

Answer 2

\[3f(\frac{1}{-2})+\frac{2 f(-2)}{-2}=(-2)^2 \text{ from putting } x=-2 \\ 3f(-2)+\frac{2 f(\frac{-1}{2})}{\frac{-1}{2}}=(-\frac{1}{2})^2 \text{ from putting } x=\frac{-1}{2}\]
looks like