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Given two functions $f=f(x)$ and $g=g(x)$ and a constant $a$, we all know from the associativity property that $$a(f\ast g)(x)=((af) \ast g)(x)$$ Let's assume that $a=a(x)$, then I would like to determine the following equality $$a(f\ast g)(x)=g(\tilde{f}\ast a)(x)$$ but $\tilde{f}$ is unknown. Is there a way to determine $\tilde{f}$?

I've seen somewhere that $\tilde{f} = \overline{f(-x)}$ but the source is not reliable and the proof is not given.

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