Continuous Compositions

Continuous Compositions

If $f$ and $g$ are continuous at $c$, then $f(g(x))$ and $g(f(x))$ are continuous at c And ${\lim }_{x\to c}g(x)=b$ Then ${\lim }_{x\to c}f(g(x))=f({\lim }_{x\to c}g(x))=f(b)$