The period of the function f(x)= [6x+7]+...

The period of the function `f(x)= [6x+7]+cospix-6x ,` where `[dot]` denotes the greatest integer function is:

A

3

B

`2pi`

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

C

`f(x)=[6x+7]+cos pi x -6x`
`=[6x] +7+cos pi x -6x`
`=7+cos pi x -{6x}`
`{6x}` has period `1//6 and cos pi x` has period 2. Then, Period of `f(x) =LCM " of " 2 " and " 1//6 =2`
Hence, the period is 2.

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