Question

Assertion (A) : If $T_1$ is the period of the function$y=e^{3(x-[x\left]\right)}$ and $T_2$ is the period of the function $y=e^{3x-\left[3x\right]}$ then $T_1=3T_2$ ([.] denotes the greatest integer function).
Reason (R) : Period of $f\left(ax\right)=\frac{T}{|a|}$

• A. Both A and R are individually true and R is the correct explanation of A
• B. Both A and R are individually true but R i s not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are individually true and R is the correct explanation of A

We know period of $x-\left[x\right]=\left\{x\right\}$ is $1$.
Thus period of $e^{3(x-[x\left]\right)}=e^{3\left\{x\right\}}$ is $1$ and period of $e^{(3x-[3x\left]\right)}=e^{\left\{3x\right\}}$ is $\frac{1}{3}$
Since period of $f\left(ax\right)$ is $\frac{T}{a}$ if period of $f\left(x\right)$ is $T$.
Hence both statements are correct and Assertion is followed by Reason.