# What is the domain and range of f(x) = 3+2sinx?

Jan 31, 2017

$\text{The Domain = "RR," and, Range = } \left[1 , 5\right]$.

#### Explanation:

We will restrict our discussion in $\mathbb{R}$.

In $\sin x$, we can take any real no. as $x ,$ which means that, the

Domain of $f$ is $\mathbb{R} .$

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

Multiplying by $2 > 0 , - 2 \le 2 \sin x \le 2 ,$ &, adding $3$,

$- 2 + 3 \le 3 + 2 \sin x \le 2 + 3 \Rightarrow 1 \le f \left(x\right) \le 5.$

$\therefore \text{ The Range of "f" is } \left[1 , 5\right]$.

Enjoy Maths.!