Find all functions $f: \mathbb{R}\setminus\{0\} \to \mathbb{R}$ satisfying $3f(x) - f\left(\frac{1}{x}\right) = x^2$.
What I did was first plug in $x = 1$ to get $2f(1) = 1 \implies f(1) = \frac{1}{2}$. Then seeing as how this looks symmetric I did the substitution $x \mapsto \frac{1}{x}$ to get $3f(\frac{1}{x})-f(x) = \dfrac{1}{x^2}$ then we can solve for $f(x)$ to get $8f(x) = 3x^2+\dfrac{1}{x^2} \implies f(x) = \frac{1}{8}(3x^2+\frac{1}{x^2})$.