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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- Oct 20th 2009, 04:07 PMgixxer998Show 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). - Oct 20th 2009, 05:42 PMhjortur
If $\displaystyle \lim\limits_{x\to a}g(x)=L$

then $\displaystyle \lim\limits_{x\to a}f(g(x))=f(L)$ if and only if

f is continuous at x=L.