Question

How do you find the domain and range of `y=(3x-2)/(4x+1)`?

Answer 1

`x inRR,x!=-1/4`
`y inRR,y!=3/4`

Explanation:

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

`"solve "4x+1=0rArrx=-1/4larrcolor(red)"excluded value"`

`rArr"domain is "x inRR,x!=-1/4`

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

`rArry(4x+1)=3x-2`

`rArr4xy+y=3x-2`

`rArr4xy-3x=-2-y`

`rArrx(4y-3)=-2-y`

`rArrx=(-2-y)/(4y-3)`

`"solve "4y-3=0rArry=3/4larrcolor(red)"excluded value"`

`"range is "y inRR,y!=3/4`