Question

What is the domain and range of `y=5/(x-1)`?

Answer 1

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

Explanation:

`"the denominator of y cannot equal 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`

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

`rArry(x-1)=5`

`rArrxy-y=5`

`rArrxy=5+y`

`rArrx=(5+y)/y`

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

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