The function is defined by p(x)= cases |x|, & x<0

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The function pp is defined by p(x)={∣x∣,x<0,⌊x⌋,0≤x<1,1x,x≥1.p(x)=\begin{cases} |x|, & x<0,\\ \lfloor x \rfloor, & 0\le x<1,\\ \dfrac{1}{x}, & x\ge 1. \end{cases} Which of the following statements correctly describes pp? (a) A single rational function defined on R∖{0}\mathbb R\setminus\{0\} (b) A piecewise function whose segments are modulus, identity and rational functions (c) A piecewise function whose three segments are respectively modulus, greatest–integer and rational functions (d) A piecewise function whose segments are modulus, greatest–integer and logarithmic functions

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