First slide

Functions (XII)

Question

$If f (x) is odd function and f (1) = a, and f (x + 2) = f (x) + f (2) then the value of f (3) is$

Moderate

A

$6 a$
B

0
C

$9 a$
D

$3 a$

Solution

$\begin{array}{l} Put x = - 1 \\ \Rightarrow f (1) = f (- 1) + f (2) \\ \Rightarrow f (1) = - f (1) + f (2) \\ \Rightarrow f (2) = 2 a \\ Now put x = 1 \\ \Rightarrow f (3) = f (1) + f (2) = a + 2 a = 3 a \end{array}$

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