a) using the definition of the continue, the definition of limit.
b) using the definition of the continue, the definition of limit.
c) using the definition of the limit, and use the result from question (a) and question (b). Because g(x) is the basic function which has a relationship with x directly, and f(g(x)) is a function about g(x), so we should use g(x) to find the relationship between f(g(x)) and x, so firstly we using the definition of limit find out the relationship between g(x) and x, and figure out the epsilon and delta, and then using the definition of limit again, find the new epsilon and new delta of f(g(x)), and compare two epsilons and two deltas, and find out the result.