How do I find if a f[g(x)] function is continuous at a certain point?

Question

anonymous · Answer

calculate its limit when g(x) approaching your point from left, then calculate it from right, if these two are equal to the value of f(g(x)) when g(x)=a, your function is continues

anonymous · Answer

Yeah I think I might just get it now. Thank you very much.

anonymous · Answer

so if your certain point is say a. then your function is continues if $$\lim_{g(x) \rightarrow a^-} f(g(x)) = \lim_{g(x) \rightarrow a^+} f(g(x)) = f(a)$$

anonymous · Answer

sure you need to find the x for which g(x)=a

anonymous · Answer

This is what the problem looks like |dw:1319412772811:dw| with the points on the left side being (-2,-1) and (0,1) and on the right side (0,2). So I would need to find the limit of those points and then insert the x when needed?. because the question is "Is f[g(x)] continuous at x = 0? I tried to give you a mental picture.