Question

If a function F is such that F(0)= 2, F (1) = 3, F (x + 2) = 2 F(x) – F (x -1) for x $\le$ 0, then F(5) is equal to

• A. -7
• B. -3
• C. 17
• D. 13

Answer 1

The correct option is D 13

We have, F(x + 2) = 2 F (x) - F (x + 1) ….. (i)
x = 0 in (1) $\Rightarrow$ F (2) = 2F (0) - F (1) = 2 (2) - 3 = 1
x = 1 in (1) $\Rightarrow$ F(3) = 2F(1) - F (2) = 2 (3) - 1 = 5
x = 2 in (1) $\Rightarrow$ F (4) = 2 F (2) - F (3) = 2 (1) - 5 = -3
x = 3 in (1) $\Rightarrow$ F(5) = 2F (3) - F (4)
= 2(5) - (-3) = 13
$\therefore$ The correct answer is (d).