Rank the following 17 functions by order of growth; that is, find a permutation (J J...

 

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Rank the following 17 functions by order of growth; that is, find a permutation (J J J7) of (1, 2, ..., 17) such that, as sets ... o(f(n)) =0(f(n)) 0(, (n)) = --- co(, (n)). 117 Then in your list, underline consecutive functions whose O-sets are equal. For example, if you think o(f(n)) 0(f(n)) = 0(f(n)) 0(f(n)) 0(3(n))=0(,(n)) then answer 5, 1, 6, 10, 3, 9 or ff.fofoff. No need to provide a proof or justification. fi(n)=nlgn f(n) = 2gn f,(n) = 500 fio (n)=n.2" f3(n)=n-2n fi(n)=2mn f(n)=2"+ f, (n) = lg (n!) f(n)=3100.2" f, (n) = n.7 f4 (n) = 3n f7 (n) = 2n f(n)=2n lgn+3n f(n)=nInn f,(n)=3"/2100 0.3 f2 (n)=lg(6n+7)x1g (5n +21) fis(n)=log, ((2n+4)(3n+2)(5n+6)) Rank the following 17 functions by order of growth; that is, find a permutation (J J J7) of (1, 2, ..., 17) such that, as sets ... o(f(n)) =0(f(n)) 0(, (n)) = --- co(, (n)). 117 Then in your list, underline consecutive functions whose O-sets are equal. For example, if you think o(f(n)) 0(f(n)) = 0(f(n)) 0(f(n)) 0(3(n))=0(,(n)) then answer 5, 1, 6, 10, 3, 9 or ff.fofoff. No need to provide a proof or justification. fi(n)=nlgn f(n) = 2gn f,(n) = 500 fio (n)=n.2" f3(n)=n-2n fi(n)=2mn f(n)=2"+ f, (n) = lg (n!) f(n)=3100.2" f, (n) = n.7 f4 (n) = 3n f7 (n) = 2n f(n)=2n lgn+3n f(n)=nInn f,(n)=3"/2100 0.3 f2 (n)=lg(6n+7)x1g (5n +21) fis(n)=log, ((2n+4)(3n+2)(5n+6))