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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