Real analysis
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(Composition of continuous Functions).Given f :A->R and g:B->R, assume that the range of f(A)={f(x):x belong to A} is contained in the domain of B so that the composition g o f(x)=g(f(x)) is well-defined on A.If f is continuous at c belong to A, and if g is continuous at f(c) belong to B, then g o f is continuous at c.
-Supply a proof for this theorem by using either the epsilon and delta characterization of continuity or the sequential characterization of continuity (If (x_n)->c (with x_n belong to A), then f(x_n)->f(c))
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Solution Summary
This is a proof regarding composition of continuous functions.
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