g: R->R

g(x) = 2 if x not equals 1

g(x) = 0 if x equals 1

f(x) = x +1 for R

"Verifiy" (sorry my english) that lim x-> 0 (gof)(x) is not equal lim x->0 (gof)(0)

If there is a contradiction with the continuity theorem of composite function, give a justification why.

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Firs part:

lim x->0 (gof)(x) = lim x->0 g(x+1) = g(1) = 2

lim x->0(gof)(0) = g(0+1) lim x->0 g(1) = 0

??

and now what is continuity theorem of composite function?