# What is the domain and range of y=-3/(4x+4)?

##### 1 Answer
Mar 28, 2017

The domain of $y$ is ${D}_{y} = \mathbb{R} - \left\{- 1\right\}$
The range of $y$, that is, ${R}_{y} = \mathbb{R} - \left\{0\right\}$

#### Explanation:

As you cannot divide by $0$,

$4 x + 4 \ne 0$

$x \ne - 1$

The domain of $y$ is ${D}_{y} = \mathbb{R} - \left\{- 1\right\}$

To find the range, we calculate ${y}^{-} 1$

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

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

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

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

$x = - \frac{3 + 4 y}{16 y}$

Therefore,

${y}^{-} 1 = - \frac{3 + 4 x}{16 x}$

The domain of ${y}^{-} 1$ is $= \mathbb{R} - \left\{0\right\}$

This is the range of $y$, that is, ${R}_{y} = \mathbb{R} - \left\{0\right\}$