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Given f (x) = 2x, g(x) = x 4, and h(x) = 5 – x 3, find (f g)(2), (h – g)(2), (f × h)(2), and (h / g)(2) This exercise differs from the previous one in that I not only have to do the operations with the functions, but I also have to evaluate at a particular x value. • for each element xof Gthere exists an element −xof G(known as the inverse of x) such that x(−x) = 0 = (−x)x(where 0 is the identity element of G) We shall usually employ multiplicative notation when discussing general properties of groups. H(n)g(n) g(n) = h(n) where h(n) is strictly increasing to ∞ 3 n > h−1(C) implies h(n) > C, which implies f(n) > C g(n) So choosing n > 1, n > k, and n > h−1(C) implies n > k ∧f(n) > C g(n).
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