Suppose that f = 2f(n/2) + n, when n is an even positive integer, and f(1) = 0. Find f(8).Select one:a.8b.64c.16d.None of the otherse.24
Question
Suppose that f = 2f(n/2) + n, when n is an even positive integer, and f(1) = 0. Find f(8). Select one:
a. 8
b. 64
c. 16
d. None of the others
e. 24
Solution
To solve this problem, we can use the method of recursion.
First, let's break down the function f(n) = 2f(n/2) + n:
- f(8) = 2f(4) + 8
- f(4) = 2f(2) + 4
- f(2) = 2f(1) + 2
We know from the problem that f(1) = 0, so we can substitute this into the equation for f(2):
f(2) = 2*0 + 2 = 2
Now we can substitute f(2) into the equation for f(4):
f(4) = 2*2 + 4 = 8
And finally, substitute f(4) into the equation for f(8):
f(8) = 2*8 + 8 = 24
So, the answer is e. 24.
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