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

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The equation max{f(x),g(x)}=1/2[(f + g) + |f - g|] represents the maximum of two real-valued functions, f(x) and g(x). The derivation involves considering two cases: when f(x) is greater than or equal to g(x), and when g(x) is greater than or equal to f(x). In the first case, |f - g| simplifies to f - g, leading to M(x) = f(x). Conversely, if g(x) is greater, |f - g| becomes g - f, resulting in M(x) = g(x). This formulation effectively captures the maximum value between the two functions.

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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
 
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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
 

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