Question

Let $f\left(x\right)=2x-\left\{\frac{x}{\pi }\right\}$ and $g\left(x\right)=\cos x$ where $\{.\}$ denotes fractional part function, then period of $gof\left(x\right)$ is:

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $\frac{3\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $\pi$

$f\left(x\right)=2x-\left(x/\pi \right)$

$g\circ f\left(x\right)=g\left(f\right(x\left)\right)=cos\left(f\right(x\left)\right)$

$g\circ f\left(x\right)=\cos (2x-(x/\pi \left)\right)$

$P(x+\pi )=\cos (2x-(x/\pi )+1)$

$P(x+\pi )=\cos (2x-(x/\pi \left)\right)=p\left(x\right)$

so, period of $g\circ f\left(x\right)$ is $\pi$