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Functions question

2020 · Shift 1 · Q33

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PYQ Library
JEE Advanced
Mathematics
Functions
2020 · Shift 1 · Q33

Functions question

2020 · Shift 1 · Q33

JEE AdvancedMathematicsFunctionsNumerical+4 / −1

Let f : [0, 2]

\to

R be the function defined by

f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)

If

\alpha ,\,\beta \in [0,2]

are such that

\{ x \in [0,2]:f(x) \ge 0\} = [\alpha ,\beta ]

, then the value of

\beta - \alpha

is ..........

Numerical answer

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