Question

If a function such that $f\left(0\right)=2;f\left(1\right)=3$ and $f\left(x+2\right)=2f\left(x\right)-f\left(x+1\right)\forall x\in R$ then f(5) =

• A. 7
• B. 13
• C. 1
• D. 5

Answer 1

The correct option is B 13

$f\left(0\right)=2,f\left(1\right)=3$ and $f(x+2)=2f\left(x\right)-f(x+1)\forall x\in R.$

at $x=0,f\left(2\right)=2f\left(0\right)-f\left(1\right)=1$

at $x=1,f\left(3\right)=2f\left(1\right)-f\left(2\right)=5$

at $x=2,f\left(4\right)=2f\left(2\right)-f\left(3\right)=-3$

at $x=3,f\left(5\right)=2f\left(3\right)-f\left(4\right)=10+3=13$