Posted by **student** on Monday, February 13, 2012 at 9:59pm.

Find the interval (or intervals) on which the given expression is defined:

(x^2-7x+12)^(1/2)

- algebra -
**Reiny**, Monday, February 13, 2012 at 10:04pm
we can write it as

√[(x-3)(x-4) ]

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**, Monday, February 13, 2012 at 10:10pm
Wouldn't they both be > or = to?

- algebra -
**Reiny**, Monday, February 13, 2012 at 10:17pm
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**, Monday, February 13, 2012 at 10:38pm
Yes you're right. THANK YOU SO MUCH!!

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