Kleinberg, Jon. Algorithm Design (p. 68, q. 5). Assume you have a positive, non-decreasing function

f

and a positive, non-decreasing function

g

such that

g(n)>=2

and

f(n)

is

O(g(n))

. For each of the following statements, decide whether you think it is true or false and give a proof or counterexample.\ (a)

2^(f(n))

is

O(2^(g(n)))

\ (b\ (c)

log_(2)f(n)

is

O(log_(2)g(n))

2. Kleinberg, Jon. Algorithm Design (p. 68, q. 5). Assume you have a positive, non-decreasing function f and a positive, non-decreasing function g such that g(n)2 and f(n) is O(g(n)). For each of the following statements, decide whether you think it is true or false and give a proof or counterexample. (a) 2f(n) is O(2g(n)) (b) f(n)2 is O(g(n)2) (c) log2f(n) is O(log2g(n))