Question

What is the domain and range of `y= 1/(x-10)`?

Answer 1

`x inRR,x!=10`
`y inRR,y!=0`

Explanation:

The denominator 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-10=0rArrx=10larrcolor(red)" excluded value"`

`rArr"domain is " x inRR,x!=10`

To find any excluded value in the range, rearrange the function making x the subject.

`rArry(x-10)=1larr" cross-multiplying"`

`rArrxy-10y=1larr" distributing"`

`rArrxy=1+10y`

`rArrx=(1+10y)/y`

`"the denominator"!=0`

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

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