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How-do-you-solve-f-3-when-f-1-1-and-f-0-1-and-f-x-f-x-1-2f-x-2-

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Question Number 135797 by benjo_mathlover last updated on 16/Mar/21
How do you solve f(3) when f(-1) = -1 and f(0) =1 and f(x) =f(x-1)-2f(x-2)?
How do you solve f(3) when f(-1) = -1 and f(0) =1 and f(x) =f(x-1)-2f(x-2)?
Answered by liberty last updated on 17/Mar/21
f(x)=f(x−1)−2f(x−2) replace x−2 by x we get 2f(x)=f(x+1)−f(x+2) (1) x=−1⇒2f(−1)=f(0)−f(1) ⇒−2=1−f(1); f(1)= 3 (2)x=0⇒2f(0)=f(1)−f(2) ⇒2 = 3−f(2); f(2)=1 (3)x=1⇒2f(1)=f(2)−f(3) ⇒6 = 1−f(3); f(3)=−5
f(x)=f(x−1)−2f(x−2)replacex−2byxweget2f(x)=f(x+1)−f(x+2)(1)x=−1⇒2f(−1)=f(0)−f(1)⇒−2=1−f(1);f(1)=3(2)x=0⇒2f(0)=f(1)−f(2)⇒2=3−f(2);f(2)=1(3)x=1⇒2f(1)=f(2)−f(3)⇒6=1−f(3);f(3)=−5

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