# What is the domain and range of f(x) = 1/(2x+4)?

Jan 28, 2017

The domain is $x \in \mathbb{R} - \left\{- 2\right\}$
The range is $f \left(x\right) \in \mathbb{R} - \left\{0\right\}$

#### Explanation:

As we cannot divide by $0$, $x \ne - 2$

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- 2\right\}$

${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to - \infty} \frac{1}{2 x} = {0}^{-}$

${\lim}_{x \to + \infty} f \left(x\right) = {\lim}_{x \to + \infty} \frac{1}{2 x} = {0}^{+}$

Therefore,

$f \left(x\right) \ne 0$

The range of $f \left(x\right)$ is ${R}_{f} \left(x\right) = \mathbb{R} - \left\{0\right\}$