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) is equal to

Step-by-step solution

f(0)=0, f(1)=1, f(2)=2 Given, f(x)=f(x-2)+f(x-3), x=3,4,5, The given function is known as "Reccurrence function". put x=3, f(3)=f(1)+f(0)=1+0=1 put x=4, f(4)=f(2)+f(1)=2+1 3 put x=5, f(5)=f(3)+f(2)=1+2 3 put x=6, f(6)=f(4)+f(3)=3+1 3+1 4 put x=7, f(7)=f(5)+f(4)=3+3 6 put x=8, f(8)=f(6)+f(5)=3+4 7 put x=9, f(9)=f(7)+f(6)=6+4 10 Hence, f(9)=10