# How do you find the domain and range for f(x)= (x+2)/(x+7)?

Nov 4, 2017

The domain is $x \in \mathbb{R} - \left\{- 7\right\}$. The range is $y \in \mathbb{R} - \left\{1\right\}$

#### Explanation:

The function is $f \left(x\right) = \frac{x + 2}{x + 7}$

The denominator must be $\ne 0$

Therefore,

$x + 7 \ne 0$, $\implies$, $x \ne - 7$

The domain is $x \in \mathbb{R} - \left\{- 7\right\}$

Let $y = \frac{x + 2}{x + 7}$

$y \left(x + 7\right) = x + 2$

$x y + 7 y = x + 2$

$x y - x = 2 - 7 y$

$x \left(y - 1\right) = 2 - 7 y$

$x = \frac{2 - 7 y}{y - 1}$

The denominator is $\ne 0$

$y - 1 \ne 0$, $\implies$, $y \ne 1$

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

graph{(x+3)/(x+7) [-32.99, 24.74, -14.6, 14.27]}