How do you find the domain of $(sqrt(9-x^2)) / (x-1)$ ?

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Answer 1 · 2015-11-01T11:42:25

$x in {[-3, 1) uu (1, 3] }$

The domain is all the possible values of $x$
To find the domain, we must find the values of $x$ for which the function is undefined

The function,

$f(x) = sqrt(9 -x^2)/(x - 1)$

will be undefined if
[1] The denominator becomes 0
[2] The term inside the square becomes negative

Hence,

$x - 1 != 0$
$=> x != 1$

$9 - x^2 > 0$

$-x^2 > -9$

$x^2 <= 9$

$=> -3 <= x <= 3$

Hence, the domain is all the real numbers between -3 and 3 except 1

How do you find the domain of (sqrt(9-x^2)) / (x-1)(sqrt(9-x^2)) / (x-1)?