Final answer:
The excluded value of the rational function f(x) = 6/(x-5) is 5, because at x = 5, the denominator becomes zero, which makes the function undefined.
Step-by-step explanation:
The student is asking to identify the excluded value of the rational function f(x) = \frac{6}{x-5}.
In a rational function, the denominator cannot be zero, because division by zero is undefined in mathematics. Therefore, to find the excluded value, we set the denominator equal to zero and solve for x.
In this case, the denominator is x - 5. We set it equal to zero:
x - 5 = 0
Solving for x gives us:
x = 5
Therefore, the excluded value for the function f(x) is 5, because when x = 5, the denominator becomes zero, which is not permitted in a rational function.