# associativity property of convolution with non-constant function

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.