Sorry reposted:
Let f(x) and g(x) be fcns defned on an interval I and let h(x) = max(f(x); g(x)) and j(x) = min(f(x); g(x)). h(x) and
j(x) are continuous on I. Show f(x) and g(x) are continuous on I or give a counterexample.
Well, we know that the function h(x) is continuous, so the max(f,g) would be continuous. I know that there are rules for algebraic combinations of continuous functions being continuous, so I'm wondering if the max function can be worked backwards to prove f and g continuous that way. Is that where you were going with this?