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

##### 1 Answer
Feb 16, 2016

The domain is the set of all real numbers $\mathbb{R}$ and the range is the interval $\left[2 , \infty\right)$.

#### Explanation:

You can plug in any real number you want into $f \left(x\right) = {x}^{2} + 2$, making the domain $\mathbb{R} = \left(- \infty , \infty\right)$.

For any real number $x$, we have $f \left(x\right) = {x}^{2} + 2 \setminus \ge q 2$. Furthermore, given any real number $y \setminus \ge q 2$, picking $x = \pm \sqrt{y - 2}$ gives $f \left(x\right) = y$. These two facts imply that the range is $\left[2 , \infty\right) = \left\{y \setminus \in \mathbb{R} : y \setminus \ge q 2\right\}$.