Solution
= Solution
If $x_n\to x$, continuity of $f$ gives $f(x_n)\to f(x)$, and continuity of $g$ at $f(x)$ then gives $g(f(x_n))\to g(f(x))$. The sequential criterion proves continuity of $g\circ f$ at $x$.
= Solution
If $x_n\to x$, continuity of $f$ gives $f(x_n)\to f(x)$, and continuity of $g$ at $f(x)$ then gives $g(f(x_n))\to g(f(x))$. The sequential criterion proves continuity of $g\circ f$ at $x$.