Mathematics

Mathematics

Problem

Define the function g:R→Rg: \mathbb{R} \to \mathbb{R} by g(x)=⌊x⌋+⌊−x⌋g(x)=\lfloor x\rfloor+\lfloor -x\rfloor. a. (i) Prove that g(x)=−1g(x)=-1 whenever xx is not an integer. b. (ii) Find the value of g(x)g(x) when xx is an integer. c. (iii) Sketch the graph of g(x)g(x) for −3≤x≤3-3\le x\le 3, clearly indicating all points of discontinuity.

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