Question

The function $(0,1)$ is periodic with period

• A. 6
• B. 3
• C. 4
• D. 12

Answer 1

Answer: (D)

12

Answer 2

$\bullet \bullet$ $\sin x$ has period $= 2 \pi$ $\Rightarrow$ $\sin \frac { \pi x } { 2 }$ has period $= \frac { 2 \pi } { \frac { \pi } { 2 } } = 4$

$\bullet \bullet$ $\cos x$ has period $= 2 \pi$ $\Rightarrow$ $\cos \frac { \pi x } { 3 }$ has period $= \frac { 2 \pi } { \frac { \pi } { 3 } } = 6$

$\Rightarrow$ $2 \cos \frac { \pi x } { 3 }$ has period = 6

$\bullet \bullet$ $\tan x$ has period $= \pi$ $\Rightarrow$ $\tan \frac { \pi x } { 4 }$ has period $= \frac { \pi } { \frac { \pi } { 4 } } = 4$ .

L.C.M. of 4, 6 and 4 =12, period of $f ( x )$ = 12.