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Maths-

General

Easy

Question

The period of the function $f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x$ where [.] de-notes the greatest integer function, is

3
$2 π$
2
$π$

hint Hint:

In this question we have to find the period of the given function. For this, we will simplify the given equation then we will find the period of each term separately. Then we know that all the terms are added in the function so the period of the whole function will be the LCM of all the periods.

The correct answer is: 2

$f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x space space space space space space space equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus left parenthesis 6 x plus 7 right parenthesis plus 7 space space space space space space space equals negative open curly brackets 6 x plus 7 close curly brackets plus cosπ x plus 7 space comma open curly brackets blank close curly brackets space i s space f r a c t i o n a l space p a r t space f u n c t i o n. P e r i o d space o f space open curly brackets 6 x plus 7 close curly brackets space i s 1 over 6 space a n d space p e r i o d space o f space space cosπ x space i s space 2. S o comma space P e r i o d space o f space f left parenthesis x right parenthesis equals L C M space o f space 1 over 6 space a n d space 2 space equals 2$

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