Question

consider the inverse cosine function, defined by ( y = cos^{-1}x ) or ( y=arccos x ). complete parts (a) through (d)
(a) what is its domain?
( -1,1 )
(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the
(b) what is its range?
(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the exp

Explanation:

Step1: Recall the range of inverse cosine function

The range of \(y = \cos^{-1}x\) is based on the principal - value range. The cosine function \(y=\cos t\) is one - to - one when \(t\in[0,\pi]\). When we find the inverse of the cosine function \(y = \cos t\) (restricted to \(t\in[0,\pi]\)), for \(y=\cos^{-1}x\), if \(x=\cos y\), the values of \(y\) that satisfy the inverse relationship (to make the inverse function well - defined) are in the interval \([0,\pi]\).

Answer:

\([0,\pi]\)