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

Aug 13, 2018

Domain: $\left(- \infty , 3\right) \cup \left(3 , + \infty\right)$
Range: $\left(- \infty , 6\right) \cup \left(6 , + \infty\right)$

#### Explanation:

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

$\frac{\left(x - 3\right) \left(x + 3\right)}{x - 3} = x + 3$

$\therefore$ $f \left(x\right) = x + 3$ with a hole at $x = 3$

So the domain is all real numbers except for $x = 3$ aka $\left(- \infty , 3\right) \cup \left(3 , + \infty\right)$

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 $\left(- \infty , 6\right) \cup \left(6 , + \infty\right)$