Consider the function f(x)={{:(x-[x]-(1)...

Consider the function `f(x)={{:(x-[x]-(1)/(2),x !inI),(0, "x inI):}` where [.] denotes the greatest integer function and I is the set of integers. Then find `g(x)max.[x^(2),f(x),|x|},-2lexle2.`

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Clearly, from graph,

`g(x)={(x^(2)",",-2 le x le -1),(-x",",-1lt x le -1//4),((1)/(2)+x",",-(1)/(4)lt x lt 0),(x",",0 le x lt1),(x^(2)",",1le x lt 2):}`

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