Question

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

Answer 1

The domain of `f(x)` is `x<=1`

Explanation:

As the range for `sin(x)` is `[-1,1]` for all real `x`

So, if we simplify the above equation:

`f(x)=arcsin(sqrt(x))` ;or
`sin(f(x))=sqrt(x)` ;or
So, we know that the range of above equation is `[-1,1]`
thus, `sqrt(x)` is `[-1,1]` ;or
`x<=1` is the solution or the domain of the original `f(x)`