Question

How do you find the domain and range of `y = { 1/ (x - 1) }`?

Answer 1

`x inRR,x!=1,y inRR,y!=0`

Explanation:

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

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

`"for the range, rearrange making x the subject"`

`rArry(x-1)=1`

`rArrxy-y=1`

`rArrxy=1+y`

`rArrx=(1+y)/y`

`"the denominator "!=0`

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