Question

If f is a function such that $f\left(0\right)=2,f\left(1\right)=3andf(x+2)=2f\left(x\right)-f(x+1)$ for every real x then f(5) is

• A. 7
• B. 13
• C. 1
• D. 5

Answer 1

The correct option is B 13

$x=0\Rightarrow f\left(2\right)=2f\left(0\right)-f\left(1\right)=2\times 2-3=1\Rightarrow x=1\Rightarrow f\left(3\right)=6-1=5$
$x=2\Rightarrow f\left(4\right)=2f\left(2\right)-f\left(3\right)=2\times 1-5=-3$
$x=3\Rightarrow f\left(5\right)=2f\left(3\right)-f\left(4\right)=2\left(5\right)-(-3)=13$ Hence (b) is correct answer.