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1)

Let   f:[0,4π][0,π]     be defined by f(x)=cos1(cosx)  . The number of points  x[0,4π]  satisfying the equation   f(x)=10x10   is 


A) 4

B) 2

C) 3

D) 1

Answer:

Option C

Explanation:

Plan

   (i)    Using definition of f(x)= cos1(x)  . we trace  the curve  f(x)=cos1(cosx) 

  (ii)   The number of solutions of an equation involving trigonometric functions and algebraic function. algebraic  and algebraic functions are found using graphs of the curves

   We know , cos1(cosx)   = {xifx[0,π]2πxifx[π,2π]2π+xifx[2π,3π]4πxifx[3π,4π]

2432021373_cos.JPG

 From above figure. it is clear that   y=10x10    and   y=cos1(cosx)  intersect  at three distinct points, so number of solution is 3.