Solution
= Solution
\b[True.] If $x_n\to x$, continuity of $g$ gives $g(x_n)\to g(x)$, and continuity of $f$ then gives
$$
f(g(x_n))\to f(g(x)).
$$
Equivalently, this is the <composition of continuous functions> theorem.
= Solution
\b[True.] If $x_n\to x$, continuity of $g$ gives $g(x_n)\to g(x)$, and continuity of $f$ then gives
$$
f(g(x_n))\to f(g(x)).
$$
Equivalently, this is the <composition of continuous functions> theorem.