Prove that if $\lim_{n \to \infty} f(x_n) = f(\lim_{n \to \infty} x_n)$ for all sequences that converge to $x$, then $f$ is continuous
How to show $f$ is continuous at $x$ IFF for any sequence ${x_n}$ in $X$ converging to $x$ the sequence $f(x_n)$ converges in $Y$ to $f(x)$