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If f(3x+2)+f(3x+29)=AAx in R , then the...

If `f(3x+2)+f(3x+29)=AAx in R ,` then the period of `f(x)` is

A

7

B

8

C

10

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`f(3x+2)+f(3x+29)=0 " (1)" `
Replacing x by `x+9`, we get
`f(3(x+9)+2)+f(3(x+9)+29)=0`
` or f(3x+29)+f(3x+56)=0 " (2)" `
From (1) and (2), we get
`f(3x+2)=f(3x+56)`
` or f(3x+2)=f(3(x+18)+2)`
Therefore, f(x) is periodic with period 54.
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