Let fx 2x 1 The smallest positive number for which fcosfx

Let f(x) = 2x - 1 The smallest positive number for which f(cos(f(x))) = 0 is x =.

Solution

f( cos(f(x)))

cos(f(x)) = cos(2x-1)

f( cos(f(x))) = 2cos(2x -1) -1 =0

2cos(2x -1) -1 =0

cos(2x-1) =1/2

2x-1 = cos^-1(1/2)

2x -1 = pi/3

2x = pi/3 +1 = (pi+3)/3

x= (pi+3)/6 = 1.02