If $$f(x)$$ and $$g(x)$$ are periodic functions with periods $$7$$ and $$11$$, respectively, then the period of $$F(x)=f(x)gx5$$−$$g(x)fx3$$ is

Question

If $$f(x)$$ and $$g(x)$$ are periodic functions with periods $$7$$ and $$11$$, respectively, then the period of $$F(x)=f(x)gx5$$−$$g(x)fx3$$ is

Infinity Learn · Accepted Answer

The period of fx is $$7$$,so the period of $$fx3$$ is $$713=21$$  since period of fx $$=$$ p then the period of $$fax+b=pasince$$ the period of $$gx=11$$, the period of $$gx5=1115=55$$  $$P1=$$ period of fx·$$gx5$$ $$=7$$ ·$$55=385and$$ $$P2=$$ period of gx·$$fx3=11$$·$$21$$ $$=231$$  therefore period of Fx $$=$$ LCM $$P1$$,$$P2$$ $$=LCM$$ $$385$$,$$231$$                                        $$=$$ $$1155$$

$If f (x) and g (x) are periodic functions with periods 7 and 11, respectively, then the period of F (x) = f (x) g (\frac{x}{5}) - g (x) f (\frac{x}{3}) is$

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If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x)=f(x)gx5−g(x)fx3 is

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$If f (x) and g (x) are periodic functions with periods 7 and 11, respectively, then the period of F (x) = f (x) g (\frac{x}{5}) - g (x) f (\frac{x}{3}) is$