If `f(x)a n dg(x)` are periodic functions with periods 7 and 11, respectively, then the period of `f(x)=f(x)g(x/5)-g(x)f(x/3)` is (a) 177 (b) 222 (c) 433 (d) 1155

Options

A. 177
B. 222
C. 433
D. 1155

Answer

D

Explanation

The period of `f(x)` is 7. So, the period of `f((x)/(3)) " is " (7)/(1//3)=21.`
The period of g(x) is 11. So, the period of `g((x)/(5)) " is " (11)/(1//5) =55.`
Hence, `T_(1)="Period of " f(x)g((x)/(5))=7xx 55=385`
and `T_(2)="period of " g(x) f((x)/(3)) =11xx 21 =231`
` :. " Period of " F(x)=LCM {T_(1),T_(2)}`
`=LCM{385,231}`
`=7xx11xx3xx5`
`=1155`