Let `f:[0,4pi]->[0,pi]` be defined by `f(x)=cos^-1(cos x).` The number of points `x in[0,4pi]` 4satisfying the equation `f(x)=(10-x)/10` is

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To solve the problem, we need to analyze the function \( f(x) = \cos^{-1}(\cos x) \) and find the number of solutions to the equation \( f(x) = \frac{10 - x}{10} \) for \( x \) in the interval \([0, 4\pi]\).

### Step-by-Step Solution:

1. **Understanding the Function \( f(x) \)**:
The function \( f(x) = \cos^{-1}(\cos x) \) gives the principal value of the cosine inverse function. The range of \( f(x) \) is \( [0, \pi] \) for \( x \in [0, 4\pi] \). This means that for every \( x \), \( f(x) \) will yield a value in the interval \( [0, \pi] \).

2. **Analyzing the Equation**:
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