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Prove that limits are equal - [Iran Second Round 1984]

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December 30, 2010
functionfloor functionalgebradomainlimitalgebra unsolved

Problem Statement

Let ff and gg be two functions such that f(x)=\frac{1}{\lfloor | x | \rfloor},   g(x)=\frac{1}{|\lfloor x \rfloor |}. Find the domains of ff and gg and then prove that lim⁡x→−1+f(x)=lim⁡x→1−g(x).\lim_{x \to -1^+} f(x)= \lim_{x \to 1^- } g(x).
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