SOLUTION: what is the domain of √ ̅ (x-3) divided by x^2-8x+12?
Algebra.Com
Question 400822: what is the domain of √ ̅ (x-3) divided by x^2-8x+12?
Found 2 solutions by nerdybill, robertb:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
"Domain" specifies the "range of values" x can take for the given function.
.
In your case, there are two conditions
- you don't want the stuff under the radical to be negative, because the square root of a negative produces an imaginary number
x-3 >= 0
x >= 3
that is, 'x' is greater than or equal to 3
.
- And, you don't want a zero in the denominator (because that produces an "undefined" number)
to find what value x can't take we set
x^2-8x+12
to zero and solve for x:
x^2-8x+12 = 0
(x+2)(x-6) = 0
x = {-2, 6}
.
Solution:
Domain x >= 3 AND "x does not = 6"
Or,
[3,6) U (6, +oo)
where
oo represents infinity
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If your rational function is , then the domain is obtained as follows:
From the expression , the critical numbers are 2, 3, and 6. These critical numbers partition the real number line into the intervals (, 2), (2, 3), (3, 6), (6, ).
At (, 2), by using the test point x = 0.
At (2, 3), by using the test point x = 2.5.
At (3, 6), by using the test point x = 4.
At (6, ), by using the test point x = 7.
The critical numbers 2 and 6 are not included in the domain, as these will make the denominator equal to 0. We want those intervals that will make , because the whole expression is under the square root symbol. The critical number x = 3 is included in the domain.
Hence the domain of the rational function is (2,3]U(6, ).
RELATED QUESTIONS
If x= √(3+√(2÷√(3−√(2) and y = 1, the value of x -y divided (answered by mananth)
what is the domain of the function y = √(x^2+... (answered by Fombitz)
what is the domain of the function f(x)= 7/(divided by)... (answered by candy423)
1/√(8x+12) what is the domain of this function? Thank you so... (answered by Gogonati)
what is the domain of... (answered by lwsshak3)
What is the domain and range of F(x,y)= √(16-x^2-16y^2 ) (answered by Edwin McCravy)
what is the domain and range of the function h(x)=... (answered by fractalier)
What is log x^2 + log √x divided by log x^2 - log √x
X means the... (answered by MathLover1)
what is the domain of... (answered by fcabanski)