How do you find the domain and range of #g(x) = (2x – 3)/( 6x - 12)#?

1 Answer
Jim G.
Aug 11, 2017

#x inRR,x!=2#
#y inRR,y!=1/3#

Explanation:

The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "6x-12=0rArrx=2larrcolor(red)" excluded value"#

To find any excluded values in the range rearrange g(x) making x the subject.

#g(x)=y=(2x-3)/(6x-12)#

#rArry(6x-12)=2x-3larrcolor(blue)" cross-multiplying"#

#rArr6xy-12y=2x-3#

#rArr6xy-2x=12y-3#

#rArrx(6y-2)=12y-3#

#rArrx=(12y-3)/(6y-2)#

#"equate denominator to zero for excluded value"#

#6y-2=0rArry=1/3larrcolor(red)" excluded value"#

#"domain is "x inRR,x!=2#

#"range is "y inRR,y!=1/3#

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