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Let f(x) = cos-1 (cos2x) and g(x) = |cos x| then

(A) number of solution of f(x) = g(x) in [0,2π] is 4.

(B) max {f(x), g(x)} is a periodic function

(C) max {f(x), g(x)} is a non differentiable function for some x,

(D) min {f(x), g(x)} is an even function

1 Answer

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Correct option  (A)(B)(C)(D)


f(x) = cos-1 (cos 2x), g(x) = |cos x|

f(x), and g(x) both are even and periodic so max {f(x), g(x)} and min{f(x), g(x)} will also be periodic and even.

but max {f(x), g(x)} will be non-differentiable when f(x) = g(x) no of points where f(x) = g(x) are four in [0, 2π] f'(x) = 0

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