First slide

Functions (XII)

Question

$If f (3 x + 2) + f (3 x + 29) = 0 \forall x \in R,$ then the period of $f (x)$ is

Moderate

A

7
B

8
C

10
D

none of these

Solution

$\begin{array}{l} f (3 x + 2) + f (3 x + 29) = 0 \\ Replacing x by x + 9, we get \\ f (3 (x + 9) + 2) + f (3 x + 56) = 0 \\ From (1) and (2), we get \\ f (3 x + 2) = f (3 x + 56) \\ or f (3 x + 2) = f (3 (x + 18) + 2) \\ Therefore, f (x) is periodic with period 54 . \end{array}$

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