The given mathematical function is:

$f(x) = \frac{1}{x - 3}$

The function $f(x)$ is undefined when the denominator is equal to zero, as division by zero is undefined in mathematics. To find the value of $x$ where the function is not defined, set the denominator equal to zero and solve for $x$:

$x - 3 = 0$ $x = 3$

Therefore, the function $f(x)$ is defined for all real numbers $x$, except $x = 3$.

In conclusion, the function is undefined for $x = 3$, and it is defined for all other real numbers.

Would you like any further details or explanations?

Here are 5 related questions for further exploration:

1. What happens to the value of $f(x)$ as $x$ approaches 3?
2. How do you find the domain of other rational functions?
3. What is the range of the function $f(x) = \frac{1}{x - 3}$?
4. Can you graph the function $f(x) = \frac{1}{x - 3}$ and identify any asymptotes?
5. How do you solve equations involving functions like $f(x) = \frac{1}{x - 3}$?

Tip: To find where a function is undefined, always look for values that make the denominator zero or result in taking an even root of a negative number.