JEE Math Practice Question
Consider the function f : R $$ \to $$ R defined by $$f(x) = \left\{ \begin{matrix} \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \\ 0,\,\,x = 0 \hfill \\\end{matrix} \right.$$. Then f is :
- A.not monotonic on ($$-$$$$\infty $$, 0) and (0, $$\infty $$)
- B.monotonic on (0, $$\infty $$) only
- C.monotonic on ($$-$$$$\infty $$, 0) only
- D.monotonic on ($$-$$$$\infty $$, 0) $$\cup$$ (0, $$\infty $$)
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