Question

How do you find the domain and range for `y=2/(5(x-2))`?

Answer 1

`x inRR,x!=2`
`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 "5(x-2)=0rArrx=2larrcolor(red)" excluded value"`

`rArr"domain is "x inRR,x!=2`

`"to find any excluded values in the range rearrange making"`
`"x the subject"`

`rArry(5x-10)=2larrcolor(blue)" cross-multipling"`

`rArr5xy-10y=2`

`rArr5xy=2+10y`

`rArrx=(2+10y)/(5y)`

`"the denominator cannot equal zero"`

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

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