JEE Advanced · 2014 · 25 May 2014 · Paper 1 · Inverse Trigonometric Functions

The function $f(x)={\cos }^{-1}(\cos x)$ has the property that $f(x)=x$ 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 $x\in [3\pi ,4\pi ]$. The line $y=\frac{10-x}{10}=1-\frac{x}{10}$ is a decreasing line from $(0,1)$ to $(10,0)$. Since $4\pi \approx 12.57$, the line intersects the domain $[0,4\pi ]$. By graphical analysis or solving in each interval, the line intersects the piecewise function at exactly 3 points.