# Proof max{f(x),g(x)}=1/2[(f + g) + |f - g|]

hi, max{f(x),g(x)}=1/2[(f + g) + |f - g|] is the equation of the maximum of two functions on the real axis. Can anyone give me a hint on how to show where this equation comes from or how it is derived

arildno
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Let M(x) be your max. function.
Suppose that, for a particular choice of x, f(x)>=g(x).
Then, |f-g|=f-g, from which follows that M(x)=f(x).
If g(x)>=f(x), then |f-g|=g-f, that is, M(x)=g(x)

cool thnx for the response