4) For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in (g(n)), or f(n) (g(n)). For each pair, determine which relationship is correct. Justify your answer. (a) f(n) = log n²; g(n) = log n+ 5. (b) f(n) = √n; g(n) = log n². (c) f(n) = log2"; g(n) = log n.
4) For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in (g(n)), or f(n) (g(n)). For each pair, determine which relationship is correct. Justify your answer. (a) f(n) = log n²; g(n) = log n+ 5. (b) f(n) = √n; g(n) = log n². (c) f(n) = log2"; g(n) = log n.
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Transcribed Image Text:4) For each of the following pairs of functions, either f(n) is in O(g(n)), f(n) is in 22(g(n)), or f(n)
(g(n)). For each pair, determine which relationship is correct. Justify your answer.
(a) f(n) = log n²; g(n) = log n+ 5.
(b) f(n)=√n; g(n) = log n².
(c) f(n) = log2"; g(n) = log n.
(d) f(n) = n; g(n) = log n.
(e) f(n) = n log n+n; g(n) = log n.
(f) f(n) = log n²; g(n) = (log n)².
(g) f(n) = 10; g(n) = log 10.
(h) f(n) = 2¹;
(i) f(n) = 2;
g(n) = 10n².
g(n) = n log n.
g(n) = 3¹.
g(n) = nº.
(j) f(n) = 2¹;
(k) f(n) = 2";
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