Question

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

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

Answer 1

The correct option is D $1155$

The period of $f\left(x\right)g\left(\frac{x}{5}\right)=7\times (11\times 5)$
The period of $g\left(x\right)f\left(\frac{x}{3}\right)=11\times 7\times 3$
Hence, period of the given expression is LCM of these two period which is $1155$