How to Prove Continuity of max{f(x), g(x)} at a Point c

[benya7thmix]

this is a problem from a sample test in my "Introduction to Real Analysis" class. i don't know how to even start thinking about this one. any hints?

Let f, g : R ! R be continuous at c, and let h(x) = max{f(x), g(x)}.

(a) Show that h(x) = (1/2) (f(x) + g(x)) + (1/2) |f(x) − g(x)| for all x in R.
(b) Show that h(x) is continuous at c.



thanks to all posters

 

[arildno]

For a) Check the two cases:
If f(x) is greater than g(x) at some point x, then h(x) should reduce to f(x).
And likewase if g(x) is greater than f(x) at the point x.

For b), what continuity properties for expressions of functions are you aware of thatmight help you?