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

Oct 8, 2017

$x$ belongs to Real numbers and $f \left(x\right)$ belongs to Real numbers too. That means that the domain belongs to $\mathbb{R}$ and the range belongs to $\mathbb{R}$.

#### Explanation:

The domain of a function are those values of $x$ where we get defined values of $y$ or $f \left(x\right)$ . The range of a function are those values of $y$ or $f \left(x\right)$ we get when $x$ is in the domain.

If we take your example into consideration->

$f \left(x\right) = x + 2$

Here, we can let $x$ be any real number and we would get a defined value for $f \left(x\right)$ .

Therefore Domain is R and Range is R.

The same cannot be said for other functions.

For example-->

Let $f \left(x\right) = {\left(x + 2\right)}^{\frac{1}{2}}$

If there is a negative number inside the root the function will not be defined. So we apply a condition-->

$x + 2 \ge 0$

Therefore
$x \ge - 2$

THIS IS THE DOMAIN. The value of $x$ has to be bigger than or equal to $\left(- 2\right)$

Now for the range, we'll put $x = - 2$ in the function.

We get $f \left(x\right) = 0$

Remember the value of $x$ always has to be bigger than or equal to $- 2$. We can let any other number bigger than $- 2$ be in the domain.

So when we put any other number (bigger than $- 2$) in $f \left(x\right)$
we will get values ranging till Infinity.

Therefore, the Range is $f \left(x\right) \in \left[0 , \infty\right)$.