SOLUTION: the domain of the function sqrt x(x-3)is write the answer in interval notation. i would also like to know what it means by write the answer in interval notation.

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Question 189454: the domain of the function
sqrt x(x-3)is
write the answer in interval notation.
i would also like to know what it means by write the answer in interval notation.
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Sqrt is undefined for negative numbers. (You need complex numbers for that). So you are being asked "for what values of x is ?"
You know that a product of two numbers is positive when both numbers are postive OR both numbers are negative. The product is negative when one number is postive and the other is negative.
You know the product is 0 when either factor is 0.
So, you can see that the points where the product is 0 are
x = 0 and x = 3
Now break the number line into three intervals.
x<0
0<=x<=3
x>3
Now, pick a value in each interval and see if that product of is positive or negative.
Let's pick x = -2
= . The product is positive, so the result is defined then.
Now pick x = 1
= . The result is negative, so the sqrt(-2) is undefined
Finally, pick x = 5.
= . again the result is positive. So the sqrt is defined.
domain is valid when
x<=0 OR x>=3
It is undefined when