JEE Advanced 2014 Mathematics question
Let f : [0, 4π] → [0, π] be defined by . The number of points x ∈ [0, 4π] satisfying the equation
f(x) =
is
Answer: 3
Solution
on [0, π], on [π, 2π], on [2π, 3π] and on [3π, 4π] (a triangular wave between 0 and π). The line falls from 1 at x = 0 to 0 at x = 10 (between 3π ≈ 9.42 and 4π) and is negative afterwards. Intersections: on [0, π]: \frac{x}{10}$ ⇒ x
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