Question

If $T_1$ is the period of the function $f\left(x\right)=e^{3(x-[x\left]\right)}$ and $T_2$ is the period of the function $g\left(x\right)=e^{3x-\left[3x\right]}$ (where $[.]$ denotes the greatest integer function) then

• A. $T_1=T_2$
• B. $T_1=\frac{T_2}{3}$
• C. $T_1=3T_2$
• D. $T_1=2T_2$

Answer 1

Answer: (C)

$T_1=3T_2$

$f\left(x\right)=e^{3(x+[x\left]\right)}=e^{3\left\{x\right\}}$

As for $\left\{x\right\}$, period is $1$

so, $T_1=1$

$f\left(x\right)=e^{3(x-[3x\left]\right)}=e^{\left\{3x\right\}}$

period$=\frac{1}{3}$

so $T_2=\frac{1}{3}$

Thus $T_2=\frac{T_1}{3}$

or $3T_2=T_1$