(x)=max{f(x),g(x)} continuous functions

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If f and g are continuous functions, then the function M(x) = max{f(x), g(x)} is also continuous. To prove this, one can use the identity max{a, b} = (a + b + |a - b|)/2, which simplifies the problem. By demonstrating that the expression (f(x) + g(x) + |f(x) - g(x)|)/2 is continuous, the continuity of M(x) can be established. This approach effectively transforms the proof into a more manageable form. The discussion concludes with an acknowledgment of understanding the proof method.
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lo,
I've got a quick q about the equation in the title, I've been asked to show/prove by analysis, that if f and g are continuous functions then M(x) is also continuous, it seems pretty intuitive but i just don't know how they want us to prove it, any help would be gr8
 
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Use the fact that max{a, b} = (a + b + |a - b|)/2.
 
how can i use this fact?
 
It transforms the problem of showing that max{f(x), g(x)} is continuous into showing that (f(x) + g(x) + |f(x) - g(x)|)/2 is continuous.
 
thx, think i get it now
 

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