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Consider the function f(x)={x-[x]-1/2,if...

Consider the function `f(x)={x-[x]-1/2,ifx !in Io,ifx in I ,w h e r e[dot]` denotes the fractional integral function and `I` is the set of integers. Then find `g(x)=m a xdot{x^2,f(x),|x|;-2lt=xlt=2.`

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Verified by Experts

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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