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Let f:[0,4pi]->[0,pi] be defined by f...

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

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

Clearly the number of solution of `f(x) =(10x)/(10)` is same as the number of points of intersection of the curves `f(x)=cos(cos^(-1)x) and y =(10-x)/(10)` in he interval `[0,4pi]`

It is evident form that the two curves intersect at three points viz a,b,c so the given equation has three solution in the interval `[0,4pi]`
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