Let f, g be real functions j and for each x Dom (f) Dom (g) define (f g)(x) :=max{f(x),g(x)} and (f

Let f, g be real functions j and for each x ˆŠ Dom (f) ˆ© Dom (g) define
(f ‹ g)(x) :=max{f(x),g(x)} and (f ‹€ g)(x) := mm{f (x), g(x)}.
a) Prove that

and

for all x ˆŠ Dom (f) ˆ© Dom (g).
b) Prove that if

exist, then (f ‹ g)(x) †’ L ‹ M and (f ‹€ g)(x) †’ L ‹€ M as x †’ a.

(f g)(x) = 2 L= limf.(x) and M= ling(x) xa