Question: Which function grows faster: f ( x ) = x 1 . 5 or g ( x ) = x ( l o g x

Which function grows faster: f

(

) = x^{1.5}

or g

(

) = x (l o g x)^{2} ?

Please give the time complexity for each of the functions, in little omega or little oh if possible, otherwise use big omega or big oh notation. Also add a small proof to your explanation.

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