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Exercise: Special Functions (Modulus,... · Q21

Q.Evaluate [3.5][3.5], [−2.3][-2.3], [7][7] and [−7][-7], where [ ⋅ ][\,\cdot\,] denotes the greatest integer function.

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Concept understanding — Modulus, Signum and Greatest Integer Functions

These three standard real functions are each defined piecewise rather than by one algebraic expression. The modulus function f(x)=∣x∣f(x)=|x| gives the non-negative magnitude of xx (domain R\mathbb{R}, range [0,∞)[0,\infty)) and its graph is a V-shaped pair of 45°45° rays meeting at the origin. The signum function reduces xx to just its sign, 11, 00 or −1-1 (domain R\mathbb{R}, range {−1,0,1}\{-1,0,1\}), graphed as three disconnected horizontal pieces. The greatest integer function [x][x] gives the greatest integer not exceeding xx (domain R\mathbb{R}, range Z\mathbb{Z}), graphed as an ascending staircase of unit-wide steps, each closed on its left and open on its right.

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