What is the domain of f(x)= arcsin[sqrt(x)]?

Sep 1, 2016

The domain of $f \left(x\right)$ is $x \le 1$

Explanation:

As the range for $\sin \left(x\right)$ is $\left[- 1 , 1\right]$ for all real $x$

So, if we simplify the above equation:

$f \left(x\right) = \arcsin \left(\sqrt{x}\right)$ ;or
$\sin \left(f \left(x\right)\right) = \sqrt{x}$ ;or
So, we know that the range of above equation is $\left[- 1 , 1\right]$
thus, $\sqrt{x}$ is $\left[- 1 , 1\right]$ ;or
$x \le 1$ is the solution or the domain of the original $f \left(x\right)$