Question

How do you find the domain and range of `1/(x-7)`?

Answer 1

`x inRR,x!=7`
`y inRR,y!=0`

Explanation:

`"let " y=1/(x-7)`

The denominator of y cannot equal zero as tis would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

`"solve " x-7=0rArrx=7larrcolor(red)" excluded value"`

`rArr" domain is " x inRR,x!=7`

`"Rearrange the function to make x the subject"`

`rArry(x-7)=1`

`rArrxy-7y=1`

`rArrxy=1+7y`

`rArrx=(1+7y)/y`

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

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