Question

The function $f\left(x\right)=min\{\sin \sqrt{\left[m\right]}x,\cos \sqrt{\left[m\right]}x\}$ has $\pi$ as fundamental period then range of $m$ is given by

• A. $[1,2)$
• B. $[3,4]$
• C. $[4,5)$
• D. $\left\{4\right\}$

Answer 1

The correct option is C $[4,5)$

Given $f\left(x\right)=min\{\sin \sqrt{\left[m\right]}x,\cos \sqrt{\left[m\right]}x\}$
$\Rightarrow f\left(x\right)=\sin \sqrt{\left[m\right]}x$

Period of $\sin \sqrt{\left[m\right]}x$ is $\frac{2\pi }{\sqrt{\left[m\right]}}$

But given period of $f\left(x\right)$ is $\pi$

$\Rightarrow \frac{2\pi }{\sqrt{\left[m\right]}}=\pi$

$\Rightarrow \sqrt{\left[m\right]}=2$

$\Rightarrow \left[m\right]=4$

Hence, $4\le m<5$