Find all functions $f:\Bbb R^+\to\Bbb R^+$ s.t. for all $x\in \Bbb R^+$ the following is valid:
$$f\bigg(\frac{1}{f(x)}\bigg)=\frac{1}{x}$$
I tried to substitute $\frac{1}{x}$ for $x$ and compare the equations: $$f\bigg(\frac{1}{f(\frac{1}{x})}\bigg)=x $$
From this I found one solution $f(x)=x.$