Find the value of f(7) is

Question

Let f: N--> N be defined by f(0) = 0 f(1) = 0 f(n+2) = 1 + f(n)

the value of f(7) is:

A/ 1

B/ 3

C/ 4

D/ 7

My guess is C. Is it correct? I understand this is the recursions and we need to calculate until it gets to the base cases, but my question is when you get the base case, how do you add up the value to get the result?

Thank You!

Answer 1

$f(7)=f(5 + 2)=1+f(5)\\f(5)=f(3+2)=1+f(3)\\f(3)=f(1+2)=1+f(1)=1+0=1$

Now just plug in the values:

$f(5)=1+1=2\\f(7)=1+2=3$

Answer 2

$f(7)=1+f(5)=1+1+f(3)=2+1+f(1)=2+1+0=3$