Find f(x) when it is given by f(x)=max...

Find f(x) when it is given by
`f(x)=max{x^(3),x^(2),(1)/(64)},AA x in [0, oo).`

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The correct Answer is:

`f(x)={{:((1)/(64)",",0ltxle(1)/(8)),(x^(2)",",(1)/(8)ltxle1),(x^(3)",",gt1x):}`

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