# What condition must be exist for this statement about real analysis to be true?

What condition must be exist for this statement about real analysis to be true? Or is it always true? please prove it.

$\max(f(x), g(x)) = \frac{f(x)+g(x)+|f(x)-g(x)|}{2}$

Hints is okay for this problem, because i have no idea how to start this proof.

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I know you get this a lot, but: What have you tried so far? –  Brett Frankel Apr 29 '12 at 1:17
@BrettFrankel - Temperory cannot even start. –  Victor Apr 29 '12 at 1:21

1. Try proving this more general statement : $$\max(a,b) = \frac{a+b + |a-b|}2$$ by treating separately the cases $a > b$ and $a \le b$.

2. Deduce your question from 1.

Hope that helps,

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