Final answer:
The domain of the function f(x)=(x / √(6-x)) is all real numbers such that x < 6. This excludes x=6 to avoid division by zero. There appears to be a slight mistake in the provided options as none exactly represents x < 6, which is the correct domain.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) which will make the function work without leading to any undefined or non-real number outputs. For the function f(x)=(x / √(6-x)), in order to find its domain, we must ensure two conditions: the denominator cannot be zero, and it cannot result in a negative value under the square root (since we cannot take the square root of a negative number in the real number system).
Therefore, √(6-x) must be greater than zero. This means that 6-x must be greater than zero, which simplifies to x<6. Since x cannot be equal to 6 (which would make the denominator zero), every real number less than 6 represents the domain of f(x). Hence, the correct option for the domain of f(x) is x < 6, not just x≠6 or x≥6.
The answer is that the domain of the function f(x)=(x / √(6-x)) is all real numbers such that x < 6. Mentioning the correct option in the final answer, the choice that matches this description is Option B. However, this is a slight mistake in the given options and the correct answer should be x < 6 which is not listed.