Question

How do you find the domain and range of `f(x) =(x+4)/(x+2)`?

Answer 1

`x inRR,x!=-2`
`y inRR,y!=1`

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) `color(blue)"undefined".`Eqating the denominator to zero and solving gives the value that x cannot be.

`"solve " x+2=0rArrx=-2larrcolor(red)" excluded value"`

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

`"to find any excluded values in the range"`

`"rearrange f(x) = y making x the subject"`

`rArry=(x+4)/(x+2)larr" cross-multiply"`

`rArry(x+2)=x+4`

`rArrxy+2y-x=4`

`rArrx(y-1)=4-2y`

`rArrx=(4-2y)/(y-1)`

`"the denominator cannot be zero"`

`"solve "y-1=0rArry=1larrcolor(red)" excluded value"`

`"range is " y inRR,y!=1`