(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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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