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Question Number 158142 by alcohol last updated on 31/Oct/21

f(x)=x−[x] where [x] is the greatest  integer function and −3≤x≤3  a) sketch f(x)  b) state the domain of f(x)  c) study the continuity of f(x) on its domain  d) state the range of f(x)

$${f}\left({x}\right)={x}−\left[{x}\right]\:{where}\:\left[{x}\right]\:{is}\:{the}\:{greatest} \\ $$$${integer}\:{function}\:{and}\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{3} \\ $$$$\left.{a}\right)\:{sketch}\:{f}\left({x}\right) \\ $$$$\left.{b}\right)\:{state}\:{the}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left.{c}\right)\:{study}\:{the}\:{continuity}\:{of}\:{f}\left({x}\right)\:{on}\:{its}\:{domain} \\ $$$$\left.{d}\right)\:{state}\:{the}\:{range}\:{of}\:{f}\left({x}\right) \\ $$

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