Consider the function f : R $ \to $ R defined by $$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.$$. Then f is :

Question

Consider the function f : R $ \to $ R defined by

$$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.$$. Then f is :

not monotonic on ($-$$\infty $, 0) and (0, $\infty $)

monotonic on (0, $\infty $) only

monotonic on ($-$$\infty $, 0) only

monotonic on ($-$$\infty $, 0) $\cup$ (0, $\infty $)

Solution

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