Question

The number of point of intersection of the curve $f\left(x\right)={\cos }^{-1}\left(\cos x\right)$ and $g\left(x\right)=\frac{20-\tan \left({\tan }^{-1}|x|\right)}{20}$ is

Answer 1

$f\left(x\right)={\cos }^{-1}\left(\cos x\right)$ and $g\left(x\right)=\frac{20-|x|}{20}=1-\frac{|x|}{20}$
$7$ point of intersection of $f\left(x\right)$ and $g\left(x\right)$ for $x>0$

Since $f\left(x\right)$ and $g\left(x\right)$, both are even functions (symmetric about Y-axis).
So, the total number of point of intersection = 2 $\times$ the point of intersection for $x>0$ $=14$