If f(x) is continuous at x = a

It is given that, f(x) is continuous at x = a.

$\therefore f(a)=\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a^{+}} f(x)$            ....(1)

Also,

$\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a^{+}} f(x)=k$                .....(2)

From (1) and (2), we have

$f(a)=k$

Thus, the value of k is f(a).

If $f(x)$ is continuous at $x=a$ and $\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a^{+}} f(x)=k$, then $k$ is equal to $f(a)$