How do you find the domain of $1/(x+2)$ ?

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Answer 1 · 2017-05-13T21:11:47

You look for the values of $x$ that are outside the domain.

If $x=-2$ then $x+2=0$ so the denominator of the fraction will become indefinite.
Other values of $x$ are acceptable, so:

Domain $x!=-2$
Or in 'the language':
$lim_(x->-2^-) y=-oo$ and $lim_(x->-2^+) y=+oo$

graph{1/(x+2) [-10, 10, -5, 5]}
As for range : as $x$ gets larger, the function will approach to $0$ .

$lim_(x->-oo) y=lim_(x->+oo) y=0$

So range: $y!=0$

How do you find the domain of 1/(x+2)1/(x+2)?