What is the domain and range of $y = 1/(x^2 - 2)$ ?

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Answer 1 · 2016-02-20T13:03:26

Domain: $(-oo,-sqrt2) uu (-sqrt2,sqrt2) uu(sqrt2, +oo)$
Range: $(-oo,-1/2] uu (0, +oo)$

The domain can be determined by equating $x^2-2=0$

solving for x:
$x=+-sqrt2$ and y is not defined when $x=+-sqrt2$

therefore the domain excludes $x=+-sqrt2$

For the Range:

$y$ can have a value from -1/2 and lower and values higher than zero.

So that Range: $(-oo,-1/2] uu (0, +oo)$

graph{y=1/(x^2-2)[-20,20,-10,10]}

have a nice day!

What is the domain and range of y = 1/(x^2 - 2)y = 1/(x^2 - 2)?