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AP EAMCET202317 May 2023Evening ShiftMathematicsFunctionsActual

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(10)=

Options

  1. A13
  2. B9
  3. C11
  4. D10

Correct answer

A. 13

Step-by-step solution

aligned & f(x)=f(x-2)+f(x-3) & f(3)=f(1)+f(0)=1+0=1 aligned aligned & f(4)=f(2)+f(1)=2+1=3 & f(5)=f(3)+f(2)=1+2=3 & f(6)=f(4)+f(3)=3+1=4 & f(7)=f(5)+f(4)=3+3=6 & f(8)=f(6)+f(5)=4+3=7 & f(9)=f(7)+f(6)=6+4=10 & f(10)=f(8)+f(7)=7+6=13 aligned

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