Functions Question 449
Question: If a function F is such that $ F(0)=2,F(1)=3, $ $ F(x+2)=2F(x)-F(x+1) $ for $ x\ge 0, $ then $ F(5) $ is equal to
Options:
A) -7
B) -3
C) 17
D) 13
Show Answer
Answer:
Correct Answer: D
Solution:
[d] We have, $ F(x+2)=2F(x)-F(x+1)… $ (i)
$ x=0in(1)\Rightarrow F(2)=2F(0)-F(1)=2(2)-3=1 $
$ x=1in(1)\Rightarrow F(3)=2F(1)-F(2)=2(3)-1=5 $
$ x=2in,(1)\Rightarrow F(4)=2F(2)-F(3)=2(1)-5=-3 $
$ x=3in(1)\Rightarrow F(5)=2F(3)-F(4)=2(5)-(-3)=13 $
$ \therefore $ The correct answer is (d).
BETA
