Question

How do you find the domain and range of `f(x) = 1/(x + 3)`?

Answer 1

`x inRR,x!=-3`
`y inRR,y!=0`

Explanation:

`"given "y=1/(x+3)`

`"the denominator cannot be zero as this would make y"`
`"undefined. Equating the denominator to zero and"`
`"solving gives the value that x cannot be"`

`"solve "x+3=0rArrx=-3larrcolor(red)" excluded value"`

`rArr"domain is "x inRR,x!=-3`

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

`rArry(x+3)=1larrcolor(blue)" cross-multiplying"`

`rArrxy+3y=1`

`rArrxy=1-3y`

`rArrx=(1-3y)/y`

`"the denominator cannot be zero"`

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

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