# How do you find the domain and range of y= 4/(x+1)?

Sep 11, 2017

The domain is $x \in \mathbb{R} - \left\{- 1\right\}$
The range is $y \in \mathbb{R} - \left\{0\right\}$

#### Explanation:

The denominator must de $\ne 0$

$x + 1 \ne 0$, $\implies$, $x \ne - 1$

The domain is $x \in \mathbb{R} - \left\{- 1\right\}$

To find the range, we proceed as follows

$y = \frac{4}{x + 1}$

$y \left(x + 1\right) = 4$

$x + 1 = \frac{4}{y}$

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

For the same reason as above,

$y \ne 0$

The range is $y \in \mathbb{R} - \left\{0\right\}$

graph{4/(x+1) [-36.54, 36.54, -18.28, 18.27]}