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 \left(\right. x \left.\right) = \frac{10

Engineering

Mathematics

Properties of Inverse Trigonometric Function

Question

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 $f (x) = \frac{10 - x}{10}$ is :

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Clearly, the equation cos^–1(cos x) $= \frac{10 - x}{10}$ has 3 solutions.