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

1 Answer
Alan P.
Apr 4, 2017

Domain: x in {RR - {-1})
Range: y in {RR - {-2}}

Explanation:

(x^2-1)/(x+1) is defined for all value of x except any value that would make the denominator equal to 0.
That is (x+1)!=0color(white)("XX")rarrcolor(white)("XX")x!=-1
(This gives us the Domain).

Notice that if x!=-1
then (x^2-1)/(x+1)=x-1
Any real number r in RR can be generated from x-1 by picking a value of x=r+1 except for the already excluded color(black)(x=-1) That is, we can not generate r=x-1 when x=-1. We can not generate r=-2.
So the Range must exclude {-2}

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