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Let f : [0, 4π] → [0,π] be defined by f(x) = cos-1(cos x).The number of points x ∈ [0, 4π] satisfying the equation f(x) = 10 - x/10 is ....

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We need to find the point of intersection of the curves f1(x) = cos-1(cos x) and f2(x) = 10 - x/10 in the domain [0, 4π].

f1(x) is a period function with period 2π and f2(x) is a straight line plotting both graphs

Therefore, A, B and C are the points of intersection of both curves which obviously satisfy the given equations, hence there are three such points.

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