# Thread: Show the limit of two composite functions aren't =

1. ## 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).

2. 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.