What is the domain and range of f(x) =( x^2 - x - 6) / (x^2 + x - 12)?

1 Answer
Shwetank Mauria
Feb 19, 2016

Domain is all values except x=-4 and x=3 range is from 1/2 to 1.

Explanation:

In a rational algebraic function y=f(x), domain means all values that x can take. It is observed that in the given function f(y)=(x^2-x-6)/(x^2+x-12), x cannot take values where x^2+x-12=0

Factorizing this becomes (x+4)(x-3)=0. Hence domain is all values except x=-4 and x=3.

Range is values that y can take. Although, one may have to draw a graph for this, but here as x^2-x-6=(x-3)(x+2) and hence

f(y)=(x^2-x-6)/(x^2+x-12)=((x-3)(x+2))/((x+4)(x-3))=(x+2)/(x+4)

= 1-2/(x+4)

and hence range is from 1/2 to 1.

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