Question

Let $f\left(x\right)=\sin \frac{\pi }{2}x$ & $g\left(x\right)=\left[x\right],$ where [.] denotes greatest integer function, then

• A. Range of $fog\left(x\right)$ & $gof\left(x\right)$ are same
• B. $gof\left(\frac{5}{2}\right)=fog\left(\frac{5}{2}\right)$
• C. $fog\left(x\right)$ & $gof\left(x\right)$ are identical functions
• D. $fog\left(x\right)$ & $gof\left(x\right)$ both are periodic with same period

Answer 1

Answer: (A), (D)

The correct options are
A Range of $fog\left(x\right)$ & $gof\left(x\right)$ are same
D $fog\left(x\right)$ & $gof\left(x\right)$ both are periodic with same period

$fog\left(x\right)=\sin \frac{\pi }{2}\left[x\right]$

$gof\left(x\right)=\left[\sin \frac{\pi }{2}x\right]$.

The range for both is $\{-1,0,1\}$

Both have the same period ,i.e 2