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Consider the function \(f: R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{ll}\left(2-\sin \left(\frac{1}{x}\ri…

Q1

Consider the function \(f: R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{ll}\left(2-\sin \left(\frac{1}{x}\right)\right)|x|, & x \neq 0 \\ 0, & x=0\end{array}\right.\). Then \(f\) is:

[JEE Main 2021, 17 Mar (Shift 2)]

a

Monotonic on \((-\infty, 0)\) only

b

Monotonic on \((-\infty, 0) \cup(0, \infty)\)

c

Monotonic on \((0, \infty)\) only

d

Not monotonic on \((-\infty, 0)\) and \((0, \infty)\)

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