Posted by student on .
Find the interval (or intervals) on which the given expression is defined:
(x^27x+12)^(1/2)

algebra 
Reiny,
we can write it as
√[(x3)(x4) ]
remember that we cannot take √ of a negative number
the critical values above are x=3 and x=4
for values between 3 and 4, the result is negative,
e.g. x = 3.5 , we get √(.5(.5)) = √.25 which is undefined.
so we need
x ≤ 3 OR x ≥ 4 
algebra 
student,
Wouldn't they both be > or = to?

algebra 
Reiny,
no, take an example of x ≤ 3
e.g. x = 5
expression is
√(8)(9) = √72 which is a real number
Trust me, my answer is correct. 
algebra 
student,
Yes you're right. THANK YOU SO MUCH!!