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 functions on the real axis. To derive this equation, consider two cases based on the relationship between f(x) and g(x). If f(x) is greater than or equal to g(x), then the absolute value simplifies to f - g, leading to M(x) = f(x). Conversely, if g(x) is greater than or equal to f(x), the absolute value simplifies to g - f, resulting in M(x) = g(x). This derivation effectively demonstrates how the equation captures the maximum value of 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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