To determine the value of [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \frac{1}{x-3} \)[/tex], we proceed as follows:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(x) = \frac{1}{x-3}
\][/tex]
So when [tex]\( x = 3 \)[/tex]:
[tex]\[
f(3) = \frac{1}{3-3}
\][/tex]
2. Simplify the expression in the denominator:
[tex]\[
f(3) = \frac{1}{0}
\][/tex]
3. Understand the implications of having zero in the denominator:
Division by zero is undefined in mathematics because it does not result in a finite number or an indeterminate form. Hence,
[tex]\[
f(3) = \text{undefined}
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is undefined.
