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What is the domain of f(x) = 1/ sqrt x - 3? slash:fraction

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shawsaws | eNotes Newbie

Posted September 5, 2013 at 12:13 AM via web

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What is the domain of f(x) = 1/ sqrt x - 3? slash:fraction

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted September 5, 2013 at 12:22 AM (Answer #1)

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Domain of:  f(x) = `1/ (sqrt(x) - 3)`

Domain is set of all possible input values for your function.

We can not have negative values as that is not a real solution for the `sqrt(x)`

Also, we can not have any values in which make our denominator equal to 0.

So far, x must be greater than or equal to 0.  However, notice if x is 9 we'd have:

`1 / (sqrt(9)-3)= 1 / (3-3) = 1/0`

Therefore x must be all real numbers greater than 0, but 9.

`{x| 0<=x<9uu 9<x<oo}`

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