# What is the range of the function f(x)=(x-3)/(x+4)?

Apr 23, 2017

$y \in \mathbb{R} , y \ne 1$

#### Explanation:

To find the value/s that y cannot be.

$\text{Rearrange to make x the subject}$

$y = \frac{x - 3}{x + 4}$

$\textcolor{b l u e}{\text{cross-multiplying ""gives}}$

$y \left(x + 4\right) = x - 3$

$\Rightarrow x y + 4 y = x - 3$

$\Rightarrow x y - x = - 3 - 4 y$

$\Rightarrow x \left(y - 1\right) = - 3 - 4 y$

$\Rightarrow x = \frac{- 3 - 4 y}{y - 1}$

The denominator cannot be zero. Equating the denominator to zero and solving gives the value that y cannot be.

$\text{solve " y-1=0rArry=1larrcolor(red)" excluded value}$

$\text{range is } y \in \mathbb{R} , y \ne 1$