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