Write the condition of the continuity of the function f(x) at the point x = a .

A function $f(x)$ is said to be continuous at the point $x=a$ if and only if the following three conditions are satisfied:

1. Existence of $f(a)$: The function $f(x)$ must be defined at $x=a$, i.e., $f(a)$ must exist.

2. Existence of the limit: The limit of the function as $x$ approaches $a$ must exist. $$\underset{x\to a}{\lim }f(x)\text{ must exist.}$$

3. Equality of the limit and the function value: The limit of the function as $x$ approaches $a$ must be equal to the function value at $x=a$. $$\underset{x\to a}{\lim }f(x)=f(a).$$

In other words, for continuity at $x=a$, the left-hand limit, right-hand limit, and the function value at $x=a$ must all be equal: $$\underset{x\to a^{-}}{\lim }f(x)=\underset{x\to a^{+}}{\lim }f(x)=f(a).$$