Answer
The statement “For the function $ f\left( x \right)=\frac{1}{x-3},f $ is not defined at $3$, so f is discontinuous at $3$” is true.
Work Step by Step
Consider the function $ f\left( x \right)=\frac{1}{x-3}$,
For a function to be continuous at a point a, the function must satisfy the following three conditions:
(a) f is defined at a.
(b) $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)$ exists.
(c) $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=f\left( a \right)$
Since the function is not defined at $3$, so the function does not satisfy the first condition of being continuous.
Therefore, the function f is discontinuous at $3$.
Hence, the statement is true.
