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?
(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fracti

Explanation:

Step1: Recall the definition of the inverse cosine function

The inverse cosine function \(y = \cos^{-1}(x)\) is the inverse of the cosine function \(y=\cos(x)\) restricted to the domain \([0,\pi]\). For a function \(y = f(x)\) and its inverse \(y = f^{-1}(x)\), the domain of \(y = f^{-1}(x)\) is the range of \(y = f(x)\).

Step2: Determine the range of the cosine function

The cosine function \(y=\cos(x)\) with \(x\in[0,\pi]\) has a range of \([- 1,1]\).

Answer:

\([-1,1]\)