# Question #4689b

##### 1 Answer
Jul 18, 2017

We will try to rearragne the formula of the function.

#### Explanation:

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

so first of all there are no constraints so the domain is : $D = x \in \mathbb{R}$

now for the range,

${\left(x - 1\right)}^{2} \ge 0 \iff {\left(x - 1\right)}^{2} + 1 \ge 1 \iff f \left(x\right) \ge 1 \iff y \ge 1$

so the range is : $R = \left[1 , + \infty\right)$