Discussion:
Q: Consider the function f(x) = arcsin(1 - x^2).
(a) What is the largest domain over which this function is defined?
(b) For this domain, what is the corresponding range of the function?
(c) If this function is one-to-one, find the inverse function f^-1(x), and state the domain of this inverse function. Otherwise, find a suitable restriction for the domain of the function, so that the restricted function has an inverse. Find this inverse function,carefully specifying its domain and range.