Functions Question 451
Question: 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
Options:
177
222
433
D) 1155
Show Answer
Answer:
Correct Answer: D
Solution:
The period of $ f(x) $ is 7. So, the period of $ f( \frac{x}{3} ) $ is $ 7 \times 3=21. $ The period of g(x) is 11. So, the period of $ g( \frac{x}{5} ) $ is $ \frac{11}{1/5}=55 $ . Hence, $ T_1= $ period of $ f(x),g,( \frac{x}{5} )=7\times 5=35 $ and $ T_2= $ period of $ g(x)f( \frac{x}{3} )= \text{lcm}(11,21)=231 $
$ \therefore $ Period of $ F(x)=LCM{T_1,T_2} $
BETA
