Generalizations list this one as a generalization of Möbius inversion formula-
Suppose $F(x)$ and $G(x)$ are complex-valued functions defined on the interval $[1, ∞)$ such that $$G(x)=\sum_{1\le n\le x} F\left(\frac xn\right)$$ then $$F(x)=\sum_{1\le n\le x} \mu(n)G\left(\frac xn\right)$$
I know the normal Möbius inversion formula with the sum running over the divisors of $n$. But, I don't see how to prove this generalized version (although I feel like it won't be that difficult). Can someone please help me out?
Hint: The proof you are asking for is provided in your referenced WikiPage in the section Proofs of generalizations.