Question

The period of function $f\left(x\right)=\left\{x\right\}+{\tan }^2\pi x+|\sin 3\pi x|$ is

• A. $\frac{1}{3}$
• B. $1$
• C. does not exist
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (B)

$1$

Period of ${\tan }^2\pi x=\frac{\pi }{|\pi |}=1$
Period of $|\sin 3\pi x|=\frac{\pi }{3\pi }=\frac{1}{3}$
Period of $\left\{x\right\}=1$ $[\because \left\{x\right\}]$ bracket function $]$
So, $f\left(x\right)=\left\{x\right\}+{\tan }^2\pi x+|\sin 3\pi x|$
$\therefore$ period of $f\left(x\right)=\frac{\text{L.C.M}(1,1,1)}{\text{H.C.F}(1,3,1)}$
$=1$