# Real analysis

(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))

https://brainmass.com/math/real-analysis/real-analysis-28571

#### Solution Summary

This is a proof regarding composition of continuous functions.

$2.19