How do you find the domain and range of $y = \frac{1}{x^{2} - 2}$ $y = 1/(x^2 - 2)$ ?

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Answer 1 · 2017-11-15T01:55:48

Domain = ${x in RR|x != +-sqrt2}$
Range = ${y in RR | y != 0}$

This will be undefined where the denominator is 0:

$x^2-2=0$
$(x-sqrt2)(x+sqrt2) = 0$
$x = +-sqrt2$

So the domain will consist of all points where x doesn't equal $+-sqrt2$

Domain = ${x in RR|x != +-sqrt2}$

Since the denominator has a higher degree than the numerator, the rational equation has a horizontal asymptote at y = 0.

This means the range will consist of all points where y doesn't equal 0

Range = ${y in RR | y != 0}$

How do you find the domain and range of y = 1/(x^2 - 2)y=1x2−2y = 1/(x^2 - 2)?