Determine the value for the following recursive method when x = 20.

Question

Question options:

1)	9
2)	4
3)	-5
4)	-4
5)	2

Answer 1

Hello, Brandon,

Were I presented with this question, I'd probably either grab a pencil and a piece of paper, or maybe write a small program. Instead, I'll use text, and develop the steps to answer it, so you can follow along. First, let's restate the problem:

Determine the value for the following recursive method when x = 20.

f(x) = f(x - 5) + 2, iff x > 9; or -2, iff x <= 9

So:

f(20) = f((20) - 5) + 2 = f(15) + 2, because x > 9

f(15) = f((15) - 5) + 2 = f(10) + 2, because x > 9

f(10) = f((10) - 5) + 2 = f(5) + 2, because x > 9

f(5) = -2, because x <= 9

Now:

f(20) = f(15) + 2

= (f(10) + 2) + 2

= ((f(5) + 2) + 2) + 2

= ((-2 + 2) + 2) + 2

= 4