Question

How do you find the Domain and Range of `f(x)=(5x-3)/(2x+1)`?

Answer 1

The domain is `x in (-oo,-1/2)uu(-1/2,+oo)`. The range is `y in (-oo, 5/2)uu(5/2,+oo)`

Explanation:

The denominator must be `!=0`

`2x+1!=0`

`x!=-1/2`

The domain is `x in (-oo,-1/2)uu(-1/2,+oo)`

To find the range, proceed as follows :

Let `y=(5x-3)/(2x+1)`

`y(2x+1)=5x-3`

`2yx+y=5x-3`

`2yx-5x=-y-3`

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

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

Here,

`2y-5!=0`

`y!=5/2`

The range is `y in (-oo, 5/2)uu(5/2,+oo)`

graph{(5x-3)/(2x1) [-16.02, 16.02, -8.01, 8.01]}