algebra

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

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

  • algebra -

    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 -

    Wouldn't they both be > or = to?

  • algebra -

    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 -

    Yes you're right. THANK YOU SO MUCH!!

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