Let f, g, h, and k be the following functions:
f(x) = 3*(x^2) + 4*ln(x) + 9
g(x) = x^2
h(x) = x^5
k(x) = 1 [the constant function "1"]
Throughout the statement and solution to this problem, a caret ("^") denotes that the number immediately following it is an exponent.
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Show the following:
(a) f = Theta(g)
(b) f = O(h)
(c) f = Omega(k)
(d) f is an unimpressive time-cost function for a sorting algorithm.