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Question 4: The function f : {0,1,2,...} → R is defined byf(0) = 7, f(n) =...

Question 4: The function f : {0,1,2,...} → R is defined byf(0) = 7,

f(n) = 5·f(n−1)+12n2 −30n+15 ifn≥1.• Prove that for every integer n ≥ 0,

f(n)=7·5n −3n2.
Question 5: Consider the following recursive algorithm, which takes as input an integer

n ≥ 1 that is a power of two:

Algorithm Mystery(n):

if n = 1
then return 1
else x = Mystery(n/2);

return n + xendif

• Determine the output of algorithm Mystery(n) as a function of n. As always, justify your answer.

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