Question

consider the inverse cosine function, defined by ( y = cos^{-1}x ) or ( y=arccos x ). complete parts (a) through

(a) what is its domain?

( -1,1 )

(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed u

(b) what is its range?

(type your answer in interval notation. simplify your answer. type an exact answer, using ( pi ) as needed. us

Explanation:

Step1: Recall the range of the inverse cosine function

The inverse cosine function \(y = \cos^{-1}x\) is defined such that if \(x=\cos y\), and we know that for the cosine function \(y = \cos t\), when we restrict the domain of \(y=\cos t\) to \(t\in[0,\pi]\), the function \(y = \cos t\) is one - to - one.

Step2: Determine the range

When we find the inverse of \(y = \cos t\) (with \(t\in[0,\pi]\)), for the inverse function \(y=\cos^{-1}x\), the range of \(y = \cos^{-1}x\) is the domain of the original one - to - one cosine function. So the range of \(y=\cos^{-1}x\) is \([0,\pi]\)

Answer:

\([0,\pi]\)