Let f:[0,2]\to R be the function defined by f(x)=(3-\sin (2 \\pix)) \sin (\\pix- \frac{\\pi}{4} ) -\sin (3 \\pix+ \frac{\\pi}{4} ) If \\alpha, \\beta ∈ [0,2] are such that \{x\in[0,2]: f(x) \\geq0\}=[\\alpha, \\beta], then the value of \\beta-\\alpha is _______. [JEE Adv 2020 P1]

Functions

Section: Mathematics

Question : 14 of 30

Marks: +1, -0

Let f:[0,2]→R be the function defined by
f(x)=(3−sin(2πx))‌sin(πx−

) −sin(3πx+

)
If α,β ∈ [0,2] are such that {x∈[0,2]:f(x)≥0}=[α,β], then the value of β−α is _______.

[JEE Adv 2020 P1]

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