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Question

If f(0)=1,f(1)=2 and f(x+2)=2f(x+2)+f(x+1), then.

A
f(3)=1
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B
f(4)=3
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C
f(5)=0
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D
f(6)=2
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Solution

The correct option is C f(6)=2
f(x+2)=2f(x+2)+f(x+1)
f(x+2)+f(x+1)=0
f(x+2)=f(x+1)
Now let x=0
Then
f(2)=f(1)=2

x=1
f(3)=f(2)=2

x=2
f(4)=f(3)=2

x=3
f(5)=f(4)=2

And at x=4
f(6)=f(5)=2

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