Question

How do you find domain and range for `f(x) = (4x - 7) /( 6 - 5x)`?

Answer 1

The domain is `x in (-oo, 6/5) uu(6/5, +oo)`.
The range is `y in (-oo, -4/5) uu(-4/5, +oo)`

Explanation:

The denominator must be `!=0`

`=>`, `6-5x!=0`

`=>`, `x !=6/5`

The domain is `x in (-oo, 6/5) uu(6/5, +oo)`

To find the range, let

`y=(4x-7)/(6-5x)`

`=>`, `y(6-5x)=4x-7`

`=>`, `6y-5xy=4x-7`

`=>`, `4x+5xy=6y+7`

`=>`, `x(4+5y)=6y+7`

`=>`, `x=(6y+7)/(5y+4)`

The denominator must be `!=0`

`=>`, `5y+4!=0`

`=>`, `y !=-4/5`

The range is `y in (-oo, -4/5) uu(-4/5, +oo)`

graph{(4x-7)/(6-5x) [-11.25, 11.25, -5.625, 5.625]}