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EAMCET Engineering 2010 Solved Paper

Section: Mathematics

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Question : 51 of 160

Marks: +1, -0

If

\;\; f(0)=0, f(1)=1, f(2)=2 \;\;

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

x=3,4,5,\dots

f(9)

12
13
14
10

Solution:

f(0)=0, f(1)=1, f(2)=2

Given,

f(x)=f(x-2)+f(x-3), x=3,4,5,\dots

The given function is known as "Reccurrence function".

\;\text{ put }\; x=3, f(3)\;=f(1)+f(0)

\;=1+0=1

\;\text{ put }\; x=4, f(4)\;=f(2)+f(1)

\;=2+1 \Rightarrow 3

\;\text{ put }\; x=5, f(5)\;=f(3)+f(2)

\;=1+2 \Rightarrow 3

\;\text{ put }\; x=6, f(6)\;=f(4)+f(3)

\;=3+1 \Rightarrow 3+1 \Rightarrow 4

\;\text{ put }\; x=7, f(7)\;=f(5)+f(4)

\;=3+3 \Rightarrow 6

\;\text{ put }\; x=8, f(8)\;=f(6)+f(5)

\;=3+4 \Rightarrow 7

\;\text{ put }\; x=9, f(9)\;=f(7)+f(6)

\;=6+4 \Rightarrow 10

\;\text{ Hence, }\;\;f(9)=10

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