At the end of the Wiki page on Möbius' Inversion Formula, the following relation is given:
$$ g(x) = \sum_{m=1}^\infty \frac{f(mx)}{m^\color{red}s}\quad\mbox{ for all } x\ge 1\quad\Longleftrightarrow\quad f(x) = \sum_{m=1}^\infty \mu(m)\frac{g(mx)}{m^\color{red}s}\quad\mbox{ for all } x\ge 1. $$
It seems like the value of $\color{red}s$ doesn't matter for the value of $g(x)$. Can someone explain this to me?