Question

How do you find the domain and range of `y = { x/ (x + 5) }`?

Answer 1

`x inRR,x!=-5`
`y inRR,y!=1`

Explanation:

`"the denominator of y cannot be zero as this would make y"`
`color(blue)"undefined"`

`"equating the denominator to zero and solving gives the value"`
`"that x cannot be"`

`"solve " x+5=0rArrx=-5larrcolor(red)"excluded value"`

`rArr"domain is " x inRR,x!=-5`

`"to find any excluded values in the range, rearrange the"`
`"function making x the subject"`

`rArry(x+5)=xlarrcolor(blue)" cross-multiplying"`

`rArrxy+5y=x`

`rArrxy-x=-5y`

`rArrx(y-1)=-5y`

`rArrx=-(5y)/(y-1)`

`"the denominator cannot be zero"`

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

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