Question

What is the domain and range of `1/(x+2)`?

Answer 1

`x inRR,x!=-2`
`y inRR,y!=0`

Explanation:

`"let "y=1/(x+2)`

`"the denominator of y 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+2=0rArrx=-2larrcolor(red)"excluded value"`

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

`"to find the range rearrange making x the subject"`

`rArry(x+2)=1`

`rArrxy+2y=1`

`rArrxy=1-2y`

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

`"the denominator cannot be zero"`

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