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For each real x, let f(x)=max{x,x^2,x^3,...

For each real `x`, let `f(x)=max{x,x^2,x^3,x^4}` then `f(x)` is

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Sometimes functions are defined like f(x)=max{sinx,cosx} , then f(x) is splitted like f(x)={{:(cosx, x in (0,(pi)/(4)]),(sinx, x in ((pi)/(4),(pi)/(2)]):} etc. If f(x)=max{x^(2),2^(x)} ,then if x in (0,1) , f(x)=

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