Let f:[0, 4pi] rightarrow [0, pi] be defined | vedclass

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(B) The function $f(x) = \cos^{-1}(\cos x)$ is a periodic function with period $2\pi$. In the interval $[0, 4\pi]$,the graph of $f(x)$ consists of two

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$3$

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(B) The function $f(x) = \cos^{-1}(\cos x)$ is a periodic function with period $2\pi$. In the interval $[0, 4\pi]$,the graph of $f(x)$ consists of two triangular waves. Specifically,$f(x) = x$ for $x \in [0, \pi]$,$f(x) = 2\pi - x$ for $x \in [\pi, 2\pi]$,$f(x) = x - 2\pi$ for $x \in [2\pi, 3\pi]$,and $f(x) = 4\pi - x$ for $x \in [3\pi, 4\pi]$. We need to find the number of intersection points of $f(x)$ and the line $y = 1 - \frac{x}{10}$. At $x = 0$,$f(0) = 0$ and $y = 1$. At $x = \pi \approx 3.14$,$f(\pi) = \pi \approx 3.14$ and $y = 1 - 0.314 = 0.686$. At $x = 2\pi \approx 6.28$,$f(2\pi) = 0$ and $y = 1 - 0.628 = 0.372$. At $x = 3\pi \approx 9.42$,$f(3\pi) = \pi \approx 3.14$ and $y = 1 - 0.942 = 0.058$. At $x = 4\pi \approx 12.56$,$f(4\pi) = 0$ and $y = 1 - 1.256 = -0.256$. By observing the graph,the line $y = 1 - \frac{x}{10}$ intersects the graph of $f(x)$ at $3$ distinct points in the interval $[0, 4\pi]$. Thus,the number of points is $3$.

Let $f:[0, 4\pi] \rightarrow [0, \pi]$ be defined by $f(x) = \cos^{-1}(\cos x)$. The number of points $x \in [0, 4\pi]$ satisfying the equation $f(x) = \frac{10-x}{10}$ is

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