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Continuity of functions

  1. Sep 22, 2009 #1
    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. jcsd
  3. Sep 22, 2009 #2

    HallsofIvy

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    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!
     
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