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State the domain of the following `y = sqrt(1 - x^2)/x`

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seerboldly | Student, Grade 10 | (Level 1) Salutatorian

Posted September 30, 2013 at 1:57 PM via web

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State the domain of the following `y = sqrt(1 - x^2)/x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 30, 2013 at 2:06 PM (Answer #1)

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The domain of the function `y = sqrt(1 - x^2)/x` has to be determined.

The domain of a function y = f(x) is the set of values that x can take on for which y is real and defined.

`y = sqrt(1 - x^2)/x`

For y to be real `1 - x^2 >= 0` and `x != 0`

=> `1 >= x^2`

=> `1 >= x >= -1`

The domain of the function `[-1, 1]- {0}`

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