Question

lf a function $f$ is such that $f\left(0\right)=2,f\left(1\right)=3,f(x+2)=2f\left(x\right)-f\left(x+1\right)$ for $x\ge 0$, then $f\left(5\right)$ is equal to

• A. $-7$
• B. $-3$
• C. $17$
• D. $13$

Answer 1

Answer: (D)

$13$

$f(x+2)=2f\left(x\right)-f(x+1),x⩾0$
Put $x=0,f\left(0\right)=2$
$f\left(2\right)=2f\left(0\right)-f\left(1\right)$
$f\left(2\right)=2\times 2-3$
$f\left(2\right)=1$
$f\left(3\right)=2f\left(1\right)-f\left(2\right)$
$=6-1$
$=5$
$f\left(4\right)=2f\left(2\right)-f\left(3\right)$
$=2\times 1-5$
$=-3$
$f\left(5\right)=2f\left(3\right)-f\left(4\right)$
$=2\times -(-3)$
$=13$