Question

Why is the following function continuous at every number in its domain? Is the domain all real numbers? This is the the function: (see reply)

Answer 1

\(\ \Huge F(x)=sin^{-1}(x^2-1) .\)

Answer 2

yes the domain is all real numbers. as sin function is continous for all all values of the theta then its inverse is also continous for all values of its domain

Answer 3

The domain of that function \[\ f(x)=\sin^{-1}(x^2-1) \] is simply the range of \[\ f(x)=\sin(x^2-1) .\]

As we know, the sine function has a domain of all numbers, but a bounded range, there for the sine inverse will have a bounded domain, but a range of all numbers.

@Study23