Question

What is the domain and range of `F(x)=(x+2) /( x-2)`?

Answer 1

`x inRR,x!=2`
`y inRR,y!=1`

Explanation:

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

`"solve "x-2=0rArrx=2larrcolor(red)" excluded value"`

`rArr"domain is " x inRR,x!=2`

To find any excluded value in the range rearrange f(x) making x the subject.

`y=(x+2)/(x-2)`

`rArry(x-2)=x+2larrcolor(blue)" cross multiplying"`

`rArrxy-2y=x+2larrcolor(blue)" distributing"`

`rArrxy-x=2+2ylarrcolor(blue)" collecting terms in x"`

`rArrx(y-1)=2+2ylarrcolor(blue)" factoring"`

`rArrx=(2+2y)/(y-1)`

`"the denominator cannot equal zero"`

`"solve " y-1=0rArry=1larrcolor(red)" excluded value"`

`rArr"range is " y inRR,y!=1`