Step-by-step Solution:

The statement is indeed correct and can be derived from the standard properties of the cosine function and its inverse. Here's a brief explanation: The cosine inverse function, \(\cos^{-1}(x)\), is defined for \(x \in [-1, 1]\) and returns a value in the range \([0, \pi]\). For \(-x\), the property of cosine gives: \[ \cos(\pi - \theta) = -\cos(\theta) \] Taking the inverse cosine on both sides: \[ \cos^{-1}(-x) = \pi - \cos^{-1}(x) \] This holds because the inverse cosine function is designed to return an angle in the range \([0, \pi]\), ensuring the result satisfies the conditions of the principal branch of \(\cos^{-1}(x)\).