Question

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

Answer 1

`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`