If f(3x+2)+f(3x+29)=0x in R , then the ...

If `f(3x+2)+f(3x+29)=0x in R ,` then the period of `f(x)` is (a) 7 (b) 8 (c) 10 (d) none of these

A. 7

none of these

Text Solution

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The correct Answer is:

`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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