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Will the answer be $d)none \ of \ these$ because we can't say anything without more information?

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    `we can't say anything without more information` That's correct.2017-01-24
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    The answer is (d); you should provide counterexamples for all of them to convince yourself.2017-01-24

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The floor function on $[0,2]$ is not continuous on $[0,2]$, not differentiable on $(0,2)$, and can't be inverted. So the answer is $D$.