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

[QUBStudent]

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

 

[Muzza]

Use the fact that max{a, b} = (a + b + |a - b|)/2.

 

[QUBStudent]

how can i use this fact?

 

[Muzza]

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.

 

[QUBStudent]

thx, think i get it now