Given f(x)=rootsignx-2 and g(x) = x-7 what is the domain of the quotient function?

A. (-infinity,2]
B. )-infinity,7 U (7, infinity)
C. [2,7) U (7, infinity)
D. (2,infinity)

multiple post. Already answered elsewhere

To determine the domain of the quotient function, we need to consider any restrictions on the values of x that would make the function undefined.

In this case, we have f(x) = √(x - 2) and g(x) = x - 7.

First, let's look at the denominator of the quotient function, g(x). Since g(x) = x - 7, we can see that the function is defined for all values of x. There are no restrictions or values that make the denominator zero, so we don't have to worry about division by zero.

Next, let's consider the function in the numerator, f(x) = √(x - 2). For this function, the argument of the square root must be greater than or equal to zero.

Therefore, we must have x - 2 ≥ 0. Solving this inequality, we find x ≥ 2.

Combining both the considerations from the numerator and denominator, we find that the domain of the quotient function is all real numbers greater than or equal to 2.

Therefore, the correct answer is D. (2, ∞).