Question

If f is a function such that f(0) = 2, f(1) = 3 and f(x + 2) = 2f(x) − f(x + 1) ∀ x ∈ R, then f(5) is

(A)  7 

(B)  13

(C)  1 

(D)  None of these

Answer 1

Correct option  (B) 13

Explanation :

We know that f(x + 2) = 2f(x) – f(x + 1). 

Substituting x = 0, we get

f(2) = 4 – 3 ⇒ f(2) = 1 

 Substituting x = 1, we get

f(3) = 6 – 1 ⇒ f(3) = 5

Substituting x = 2, we get

f(4) = 2 – 5 ⇒ f(4) = –3

Substituting x = 3, we get

f(5) = 10 + 3 ⇒ f(5) = 13