Prove that continuous function of a continuous function is continuous.

To prove that the composition of two continuous functions is continuous, we'll use the epsilon-delta definition of continuity. Let's suppose we have two functions, f(x) and g(x), such that f(x) is continuous at a point c, and g(x) is continuous at the point f(c). We want to show that their composition, h(x) = ____ ______ __________ _______ _________ __________ _____ _____ _______ _________ _________ ________.
_____ ________ __________ _____ _________ ______ __________ ____ ____ ____ _________ ____.
_________ _____ ____ ____ _________ __________ ______.
____ _______ ____ _________ ______ __________ __________ __________ _________ _________ ___ ____.
_______ ________ ____ ________ __________ ____ ___ _________.
___ _____ _______ ________ __________ _____ _____ ___.
______ _____ ___ ______ ___ ___ _____ _________ ____.
_________ _________ ___ _________ ___.
_____ __________ ___ _______ _______.
_________ __________ _______ _______ _______ _______ __________ ____ ___ _____ ___.
____ ______ ____ ___ _________ ___ _______ ________ ____ ___ _______.
___ _________ ________ ____ ________ _________ ____ ____.
__________ ________ _______ ____ ____ ______.
_____ _________ _____ ______ ___ ________ __________.
_________ _______ _________ __________ __________ _________ _________ __________ __________ ________ ______ __________.
_________ ________ ______ __________ _______ ________.
___ _________ ______ _________ ___ _______.
____ ________ ________ ______ __________ _______ __________ ___ __________ ___.
______ __________ _____ ____.
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