JEE Advanced 2020 Paper 1 Mathematics Q15

Mathematics

Problem

Let f : [0, 2] ⟶ ℝ be the function defined by f(x) = (3 − sin(2πx)) sin(πx − π/4) − sin(3πx + π/4). If α, β ∈ [0, 2] are such that {x ∈ [0, 2] : f(x) ≥ 0} = [α, β], then the value of β − α is _____.

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