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

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

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The correct Answer is:
`g(x)={{:(x^(2)",", -2 le x le -1),(-x",", -1 le x le -1//4),(x+1/2",", -1/4 le x le 0),(x",", 0 le x le 1),(x^(2)",", 1 le x le 2):}`
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