1. 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)). Determine which relationship is correct and briefly explain why.

a. f(n) = log n^2 ; g(n) = log n +5

b.f(n) = sqrt n ; g(n) = log n^2

c.f(n) = log^2 n ; log n

d.f(n) = n ; g(n) = log^2 n

e.f(n) = n log n + n; g(n) = log n

f.f(n) = 10 ; g(n) = log 10

g.f(n) = 2^n ; g(n) = 10n^2

h.f(n) = 2^n; g(n) = 3^n