# What is the domain of y=3/2 arcsin(2x+.5)?

##### 1 Answer
Jan 17, 2018

$- \frac{3}{4} \le x \le \frac{1}{4}$

#### Explanation:

The domain of ${\sin}^{-} 1 \left(u\right)$ is $- 1 \le u \le 1$, so for this problem we need to solve:

$- 1 \le 2 x + \frac{1}{2} \le 1$

subtracting $\frac{1}{2}$ from all parts:

$- \frac{3}{2} \le 2 x \le \frac{1}{2}$

dividing through by 2:

$- \frac{3}{4} \le x \le \frac{1}{4}$