Convolution - prove commutative

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anyone know how to prove that it is commutative...

as if f *g = g*f
 
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Try a change of variables.
 
You might want to start with the definition: the convolution of f and g is
f*g(x)= \int_0^\infty f(x-t)g(t)dt and, of course, g*f(x)= \int_0^\infty g(x-u)f(u)du (I have intentionally used a different variable of integration here). Hmm, in one you have f(x-t) and in the other f(u). Does that substitution benndamann33 mentioned leap to mind?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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