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Math Help - Show the limit of two composite functions aren't =

  1. #1
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    Show the limit of two composite functions aren't =

    R= Real numbers
    Let g be defined on R by g(1) := 0, and g(x) := 2 if x does not = 1, and let f(x) := x+1 for all x in R. Show that limit as x approaches 0, (g o f) does not equal (g o f)(0).
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  2. #2
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    If \lim\limits_{x\to a}g(x)=L
    then \lim\limits_{x\to a}f(g(x))=f(L) if and only if
    f is continuous at x=L.
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