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Question
If f(0)=1,f(1)=2 and f(x+2)=2f(x+2)+f(x+1), then.
If f(0)=1,f(1)=2 and f(x+2)=2f(x+2)+f(x+1), then.
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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=4f(6)=−f(5)=−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
f(5)=−f(4)=2
And at x=4
f(6)=−f(5)=−2
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