JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

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

A) 177

B) 222

C) 433

D) 1155

Correct Answer: D

Solution :

[d] The period of \[f(x)\] is 7. So, the period of \[f\left( \frac{x}{3} \right)\] is \[\frac{7}{1/3}=21.\]

The period of g(x) is 11. So, the period of \[g\left( \frac{x}{5} \right)=7\times 55=385\] is \[\frac{11}{1/5}=55\].

Hence, \[{{T}_{1}}=\]period of \[f(x)\,g\,\left( \frac{x}{5} \right)=7\times 55=385\]

and \[{{T}_{2}}=\] period of \[g(x)f\left( \frac{x}{3} \right)=11\times 21=231\]

\[\therefore \] Period of \[F(x)=LCM\{{{T}_{1}},{{T}_{2}}\}\]