Given f(x) = root x-2 and g(x) = x-7 what is the domain of the quotient function f/g ?
do you mean f(x) = √(x-2) or f(x) = √x - 2 ?
I will assume the first one
so the quotient function is
√(x-2)/(x-7)
Two things will affect the domain
1. x-2 ≥ 0 or x ≥ 2 to be able to take the square root.
2. x - 7 cannot be zero, or x cannot be 7, or else we are dividing by zero
so the domain is the set of all real numbers such that x ≥ 2 with x not equal to 7
The second one f(x) = �ãx - 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)
Good ? Breanna! I have been tryin to figure this one out for some time! I am going to guess and say D but lets see what everyone else says!
To find the domain of the quotient function f/g, we need to consider two things:
1. The domain of the function f(x).
2. The values of x for which g(x) is not equal to zero.
First, let's determine the domain of f(x). The function f(x) is a square root function, which means the radicand (x - 2) must be non-negative for real values of x. So, we set the radicand greater than or equal to zero:
(x - 2) ≥ 0
Solving the inequality, we find:
x ≥ 2
Therefore, the domain of f(x) is all real numbers greater than or equal to 2, or in interval notation: [2, ∞).
Next, let's consider the values of x for which g(x) is not equal to zero. The function g(x) is a linear function, and it is equal to zero when x = 7.
Therefore, the domain of the quotient function f/g consists of all the values of x where both f(x) and g(x) exist, and g(x) is not equal to zero. In this case, since the domain of f(x) is [2, ∞) and the value x = 7 makes g(x) zero, we need to exclude x = 7 from the domain.
Therefore, the domain of the quotient function f/g is [2, 7) ∪ (7, ∞).