Question

Why is the domain of inverse functions like arcsine limited to the interval [-1, 1]? What benefit comes from?

Answer 1

Look at the function of sine inverse means you are writing the equation where y becomes x and x becomes y

Answer 2

sin(x) looks like this



If we were to write it where x becomes y and y becomes x



we wouldn't have a function, as for a function to be a function it must be able to pass the vertical line test, which states if you draw a line anyhwere on the graph it should not be able to pass through the graph of the function more than once