A function satisfies the identity $f(x) + 2f\left(\frac1x\right) = 2x+1$ ... find another identity that $f(x)$ satisfies.

Question

A function satisfies the identity $f(x) + 2f\left( \frac{1}{x} \right) = 2x+1$. By replacing all instances of $x$ with $\frac{1}{x}$, find another identity that $f(x)$ satisfies.

I have absolutely no idea what this question is asking, and how to go about it. I would really appreciate some help; thanks in advance!

Answer 1

This question is asking you to replace a $\frac{1}{x}$ every where you see an $x$ in $f(x) + 2f(1/x) = 2x+1$, i.e. $f(\frac{1}{x})+2f(\frac{1}{\frac{1}{x}})=f(\frac{1}{x})+2f(x)=\frac{2}{x}+1$.