f(x)=root sign, and inside that x-2 and g(x)x-7. Which of the following 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)
Duplicate post; already answered
What was the answer? Thanks
To determine the domain of the quotient function, we need to consider the restrictions of both f(x) and g(x).
The function f(x) = √(x-2) has a square root. The square root function is only defined for non-negative values, so x-2 must be greater than or equal to 0. Therefore, the domain of f(x) is x >= 2.
The function g(x) = x-7 does not have any restrictions. It can take any real number as its input.
When we divide f(x) by g(x), we need to be careful of dividing by zero. In this case, we need to make sure that g(x) ≠ 0.
Since g(x) = x-7, it will be equal to zero when x = 7. Therefore, we cannot include x = 7 in the domain of the quotient function.
Combining the restrictions from f(x) and g(x), the domain of the quotient function will be all values of x that satisfy x ≥ 2 and x ≠ 7.
So, the correct answer is C. [2,7) U (7,infinity).