What is the answer? I came up with C. is this correct? Thanks for the help in advance!
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 f/g?
A. (-infinity,2]
B. (-infinity,7) U (7,infinity)
C. [2,7) U (7,infinity)
D. (2, infinity)
sqrt(x-2) /( x-7) ???
x must be 2 or greater or we have the square root of a negative number, which is not real.
x may not be 7 or we have a zero in the denominator
therefore
2 to 7 and 7 to + infinity
Is C the answer?
Math - Kim, Friday, June 19, 2009 at 10:42pm
Is C the quotient function of f/g?
for g(x) = x-7
only allowing real numbers...
Yes, C is the answer.
Thank yoU!
To find the domain of the quotient function f/g, you need to consider two things:
1. The domain of the numerator function f(x) = sqrt(x-2):
Since we have the square root of (x-2), the radicand (x-2) must be greater than or equal to 0. This means x-2 ≥ 0, so x ≥ 2. Therefore, the domain of the numerator function is x ≥ 2.
2. The domain of the denominator function g(x) = x-7:
To avoid a zero in the denominator, we need to exclude the value of x that makes the denominator equal to 0. So, x ≠ 7.
Now, we need to find the common domain of these two functions. Since f(x) = sqrt(x-2) requires x ≥ 2 and g(x) = x-7 requires x ≠ 7, we can combine these restrictions. The common domain is x ≥ 2 and x ≠ 7.
Looking at the answer choices:
A. (-infinity,2] - This option includes values less than 2, which is not part of our domain.
B. (-infinity,7) U (7,infinity) - This option includes x < 2, which is not part of our domain.
C. [2,7) U (7,infinity) - This option includes the correct range of values: x ≥ 2 and x ≠ 7.
D. (2, infinity) - This option only includes x > 2, which is not part of our domain.
Therefore, the correct answer is C. [2,7) U (7,infinity).