# How do you find the domain and range of f(x)= (2x^2+7x-15) / (x+5)?

May 17, 2018

$x \in \mathbb{R} , y \in \mathbb{R}$

#### Explanation:

$\text{factorise and simplify by cancelling}$

$f \left(x\right) = \frac{\left(2 x - 3\right) \cancel{\left(x + 5\right)}}{\cancel{x + 5}} = 2 x - 3$

$f \left(x\right) \text{ simplifies to a linear expression which has no }$
$\text{restrictions on it's domain and hence no restrictions}$
$\text{on it's range}$

$\Rightarrow \text{domain } x \in \mathbb{R}$

$\Rightarrow \text{range } y \in \mathbb{R}$
graph{(2x^2+7x-15)/(x+5) [-10, 10, -5, 5]}