Question

How do you find the domain and range of `(5x-3) / (2x +1)`?

Answer 1

`x inRR,x!=-1/2`
`y inRR,y!=5/2`

Explanation:

`"the domain is defined for all real values of x except for"`
`"values of x which make the denominator equal zero"`

`"to find the value that x cannot be, equate the denominator"`
`"to zero and solve"`

`"solve "2x+1=0rArrx=-1/2larrcolor(red)" excluded value"`

`rArr"domain is "x inRR,x!=-1/2`

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

`y=(5x-3)/(2x+1)" making x the subject"`

`rArry(2x+1)=5x-3larrcolor(blue)" cross-multiplying"`

`rArr2xy+y=5x-3`

`rArr2xy-5x=-3-y`

`rArrx(2y-5)=-(3+y)`

`rArrx=-(3+y)/(2y-5)`

`"the denominator cannot equal zero"`

`"solve "2y-5=0rArry=5/2larrcolor(red)" excluded value"`

`rArr"range is " y inRR,y!=5/2`