Question

if f(0)=0,f(1)=1,f(2)=2 and f(x)=f(x-2)+f(x-3) for x=3,4,5,....then f(9)=

Answer 1

Answer:

f(9) = 10

Step-by-step explanation:

Here, the functional variable is 'x' and we need to find the value f(9). We neeed to substitute the f(x) value in the given expression

f(x) = f(x - 2) + f(x -3)

f(9) = f(9 - 2) + f(9 - 3)

f(9) = f(7)  + f(6)

f(9) = f(7 - 2) + f(7 - 3) + f(6- 2) + f(6-3)

f(9) = f(5) + f(4) + f(4) + f(3)

f(9) = f(5 - 2) + f(5 - 3) +2 X f(4 - 2) + f(4 - 3) + f (3)

f(9) = 2 X f(3) +f(2) +  2 x f(2) + f(1)

f(9) = 2 X f(3 - 2) + f(3 - 3) + 2 + 2 x ( 2 + 1)

f(9) = 2 X f(1) + f(0) + 2 + 2 X 3

f(9) = 2 X 1 + 0 + 8

f(9) = 2 + 8 = 10