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If f(f(n))+f(n)=2n+3 and f(0)=1, what is the value of f(2012)?

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a) 2011              b) 2012                    c) 2013                    d) 4095
asked Oct 30, 2013 in TCS by Campusgate

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Put n = 0
Then f(f(0))+f(0) = 2(0) + 3 $ \Rightarrow $ f(1) + 1 = 3 $ \Rightarrow $ f(1) = 2
Put n = 1
f(f(1)) + f(1) = 2(1) + 3 $ \Rightarrow $ f(2) + 2 = 5 $ \Rightarrow $f(2) = 3
Put n = 2
f(f(2)) + f(2) = 2(2) + 3 $ \Rightarrow $ f(3) + 3 = 7 $ \Rightarrow $ f(3) = 4
......
f(2012) = 2013

Option C

answered Oct 30, 2013 by Campusgate
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