Question

Find domain and range of f(x)=x²-9/x-3?

Answer 1

Domain: `(- oo,3)uu(3, +oo)`
Range: `(-oo,6)uu(6, +oo)`

Explanation:

If you factor the numerator, you can see that you will have terms that cancel out:

`((x-3)(x+3))/(x-3)=x+3`

`therefore` `f(x)=x+3` with a hole at `x=3`

So the domain is all real numbers except for `x=3` aka `(-oo,3)uu(3, +oo)`

Plug in three for `x` to find out where the range doesn't exist:

`y=6`

So, the range is all real numbers except for `y=6` aka `(-oo,6)uu(6, +oo)`