Question

How do you find the domain and range of `g(x)= 2/ (x-1)`?

Answer 1

`"domain " x inRR,x!=1`

`"range " y inRR,y!=0`

Explanation:

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

`"solve " x-1=0rArrx=1larrcolor(red)" excluded value"`

`rArr"domain " x inRR,x!=1`

`"To find the excluded value/s in the range"`

`"Rearrange g(x) and make x the subject"`

`g(x)=y=2/(x-1)larrcolor(blue)" cross-multiply"`

`y(x-1)=2`

`xy-y=2`

`xy=2+y`

`rArrx=(2+y)/y`

`" the denominator cannot be zero"`

`rArry=0larrcolor(red)" excluded value"`

`rArr"range " y inRR,y!=0`
graph{2/(x-1) [-10, 10, -5, 5]}