# How do you find the domain and range of f(x) = x^2 + 1?

Feb 16, 2016

Domain: $\mathbb{R}$
Range: $\mathbb{R} \ge 1$

#### Explanation:

$f \left(x\right) = {x}^{2} + 1$ is defined for all Real values of $x$;
therefore the Domain of $f \left(x\right)$ is all Real values (i.e. $\mathbb{R}$).

${x}^{2} \ge 0$ for all Real values of $x$
$\rightarrow {x}^{2} + 1 \ge 1$ for all Real values of $x$
therefore the Range of $f \left(x\right)$ is all Real values $\ge 1$