Answer :

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.