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Question Number 36104 by rahul 19 last updated on 28/May/18
$$\mathrm{If}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{R}}\rightarrow\boldsymbol{\mathrm{R}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid\:\mathrm{f}\left({x}\right)\:−\:\mathrm{f}\left(\mathrm{y}\right)\mid\:\leqslant\:\mid\:\mathrm{sin}\:{x}\:−\:\mathrm{sin}\:\mathrm{y}\:\mid\forall{x},\mathrm{y}\in\mathbb{R}, \\ $$$$\mathrm{Then}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Bijective} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{many}−\mathrm{one} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{periodic} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{non}−\mathrm{periodic} \\ $$
Commented by rahul 19 last updated on 31/May/18
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