# Question #b1c7e

Mar 22, 2017

The Range is $\left[0 , 2\right] = \left\{x \in \mathbb{R} : 0 \le x \le 2.\right\}$

#### Explanation:

Observe that, $\forall x \in \mathbb{R} , - 1 \le \sin x \le 1.$

Adding $1$ throughout the inequality, we have,

$\forall x \in \mathbb{R} , - 1 + 1 \le \sin x + 1 \le 1 + 1 , i . e . ,$

$\forall x \in \mathbb{R} , 0 \le F \left(x\right) \le 2.$

Hence, the Range is $\left[0 , 2\right] = \left\{x \in \mathbb{R} : 0 \le x \le 2.\right\}$