Answer:
First blank: [-π/2 , π/2]
Second blank: [-π/2 , π/2]
Explanation:
The conditions for inverse function to exist is that the function should be one to one function.
A function for which every element of the range of the function corresponds to exactly one element of the domain.
The function can be tested by the vertical line test.
For the given function f(x) = sin x is not one to one function.
so, the domain of the function f(x)=sin x restricted so that its inverse function exists
The domain will be the range provided that when we apply the vertical line test will intersects at only one point
So, the domain will be [-π/2 , π/2]
And this means f(x) = sin⁻¹ x are on the interval [-π/2 , π/2]