Question

A function f(x) is defined for all real x and satisfied f(x + y) = f(xy) ∀x, y. If f(1) = −1, then f(2006) equals

(A)  −2006 

(B)  2006

(C)  −1

(D)  None of these

Answer 1

Correct option  (c) -1

Explanation :

f(x + y) = f(xy) ∀ x, y

 Put

x = y = 1  ⇒ f(2) = f(1)

Similarly, 

f(2) = f(1) = f(3) =....=f(20006) = -1