For this written assignment, answer the following questions showing all of your work.
1. Find the domain of the function using interval notation.
x−6
f ( x )= √
√ x−4
Domain: [6, ∞)
Explanation:
The domain is the value of x.
we look at the restriction on the numerator and denominator. The x value should be at
least 6 to make the statement correct, else this will make it as complex number resulting
the numerator with complex number.
When x = 6, our numerator would be 0, this will make f(x) = 0
however, if x = 5, our numerator will be −1
which is an imaginary number I, hence the value of x should be at least 6 to have a real
number answer.
Interval notation: [6, ∞)
Using the denominator
√ x−4=0
√ x−√ 4=0
√ x−2=0
√ x−2+2=0+2 (add 2 to both sides to solve x
1. Find the domain of the function using interval notation.
x−6
f ( x )= √
√ x−4
Domain: [6, ∞)
Explanation:
The domain is the value of x.
we look at the restriction on the numerator and denominator. The x value should be at
least 6 to make the statement correct, else this will make it as complex number resulting
the numerator with complex number.
When x = 6, our numerator would be 0, this will make f(x) = 0
however, if x = 5, our numerator will be −1
which is an imaginary number I, hence the value of x should be at least 6 to have a real
number answer.
Interval notation: [6, ∞)
Using the denominator
√ x−4=0
√ x−√ 4=0
√ x−2=0
√ x−2+2=0+2 (add 2 to both sides to solve x
