Let . Which of the following statement(s) is/are…

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let f(x)=sin⁡−1∣sin⁡x∣+cos⁡−1(cos⁡x)f(x) = \sin^{-1} |\sin x| + \cos^{-1} (\cos x) . Which of the following statement(s) is/are TRUE? (1) f(f(3))=πf(f(3)) = \pi (2) f(x)f(x) is periodic with fundamental period 2π2\pi (3) f(x)f(x) is neither even nor odd (4) Range of f(x)f(x) is [0,2π][0, 2\pi]

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