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What is the domain of the function that is given by `f(x) = sqrt ((x^2 - 16)/(x + 2))`

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homeschool11 | Salutatorian

Posted February 10, 2012 at 1:28 AM via web

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What is the domain of the function that is given by `f(x) = sqrt ((x^2 - 16)/(x + 2))`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 10, 2012 at 2:18 AM (Answer #1)

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The function f(x) = `sqrt ((x^2 - 16)/(x + 2))`

The square root function sqrt x, has a real value for x greater than or equal to 0

`(x^2-16)/(x - 2) >= 0`

=> `((x - 4)(x + 4))/(x - 2) >= 0`

=> `(x - 4)(x + 4) >= 0`

This is possible when either `x - 4 >= 0` and `x + 4 >= 0` or when `x - 4 <= 0` and `x + 4 <= 0`

=> `x >= 4` and `x >= -4` or `x <= 4` and `x <= -4`

The domain of the function is the set is {-inf., -4]U[4, inf.}

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