# Continuity of functions

1. Sep 22, 2009

### dannysaf

1)Let f and g be functions such that f (x) + g(x) and f (x) − g(x) are
continuous at x = x0 . Must f and g be continuous at x = x0 ?

2)What can be said about the continuity of f (x) + g(x) at x = x0 , if
f (x) is continuous and g(x) is discontinuous at x = x0 ?

3)What can be said about the continuity of f (x)g(x) at x = x0 , if
f (x) is continuous and g(x) is discontinuous at x = x0 ?

2. Sep 22, 2009

### HallsofIvy

Re: Continuity

I think the facts that f(x)= ((f+g)(x)+ (f-g)(x))/2 and g(x)= ((f+g)(x)- (f-g)(x))/2 will help a lot!