Sure, let's evaluate the given function step-by-step.
We are given the function:
[tex]\[ f(x) = \frac{x}{x-2} \][/tex]
We need to evaluate this function at [tex]\( x = 6 \)[/tex].
1. Substitute [tex]\( x = 6 \)[/tex] into the function:
[tex]\[ f(6) = \frac{6}{6 - 2} \][/tex]
2. Simplify the expression in the denominator:
[tex]\[ 6 - 2 = 4 \][/tex]
So, the function becomes:
[tex]\[ f(6) = \frac{6}{4} \][/tex]
3. Simplify the fraction:
[tex]\[ \frac{6}{4} = \frac{3}{2} \][/tex]
Therefore, the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 6 \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
So, the correct answer is:
(A) [tex]\( \frac{3}{2} \)[/tex]
