Let `f:[0,4pi]vec[0,pi]` be defined by `f(x)=cos^(-1)(cosx)dot` The number of points `x in [0,4pi]s a t i sfy ingt h e` equation `f(x)=(10-x)/(10)` is____

Answer

3

Explanation

`f: [0, 4pi] rarr [0, pi], f(x) = cos^(-1) (cos x)`
For number of roots of equation `cos^(-1) (cos x) = (10 -x)/(10)`, draw the graph of `y = cos^(-1) (cos x)`
and `y = (10 -x)/(10)` and find the points of intersection.

From the graph number of solution is 3