Question

How do you find the domain and range of `f(x) = 5/(x-9)`?

Answer 1

`x inRR,x!=9`
`y inRR,y!=0`

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

`"solve "x=9=0rArrx=9larrcolor(red)"excluded value"`

`rArr"domain is "x inRR,x!=9`

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

`y=5/(x-9)`

`"multiply both sides by "(x-9)`

`rArry(x-9)=5`

`rArrxy-9y=5`

`rArrxy=5+9y`

`rArrx=(5+9y)/y`

`"the denominator cannot equal zero"`

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

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