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

##### 1 Answer
Oct 20, 2017

$x \in \mathbb{R}$ and $f \left(x\right) \in \mathbb{R}$
OR
$x \in \left(- \infty , + \infty\right)$ and $f \left(x\right) \in \left(- \infty , + \infty\right)$

#### Explanation:

The domain is the set of all possible $x$-values which will make the function "work", and will output real $f \left(x\right)$-values.

So when we have the function $f \left(x\right) = - \frac{x}{2}$ we can let $x$ be any real number and we will always get a real and defined value of $f \left(x\right)$.
Therefore the domain is $\mathbb{R}$.

The range is the resulting $f \left(x\right)$-values we get after substituting all the possible $x$-values.

Here too, all the possible values of $f \left(x\right)$ are all the real numbers.
Therefore the range is also $\mathbb{R}$.

Example -->

Let $x = \sqrt{2}$ which is a real number.
then we'd get $f \left(x\right) = - \frac{\sqrt{2}}{2}$ which is also a real number.