Asked by student
Find the interval (or intervals) on which the given expression is defined:
(x^2-7x+12)^(1/2)
(x^2-7x+12)^(1/2)
Answers
Answered by
Reiny
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
√[(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
Answered by
student
Wouldn't they both be > or = to?
Answered by
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.
e.g. x = -5
expression is
√(-8)(-9) = √72 which is a real number
Trust me, my answer is correct.
Answered by
student
Yes you're right. THANK YOU SO MUCH!!
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