Find all functions $f:\mathbb{R^*}\to\mathbb{R^*}$ that satisfy $$f(x)f(\frac{1}{x})=1\hspace{1 em}\forall x\in\mathbb{R^*}$$
I only found that every function $f(x)=x^n, n\in\mathbb{N^*}$ is a solution. Can you find all the solutions to this?
2026-03-26 20:16:50.1774556210
$f(x)f(\frac{1}{x})=1\hspace{1 em}\forall x\in\mathbb{R}$
58 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FUNCTIONS
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