Question

Find the range of $f\left(x\right)=\frac{\sin \left(\pi [x^2+1]\right)}{x^4+1}$ where $[.]$ is greatest integer function

• A. $[0,1]$
• B. $[-1,1]$
• C. $0$
• D. None of these

Answer 1

Answer: (C)

$0$

Since $[x^2+1]$ is an integer
$\therefore \sin \left(\pi [x^2+1]\right)=0$
$\Rightarrow f\left(x\right)=\frac{\sin \left(\pi [x^2+1]\right)}{x^4+1}=0$
Hence, Range of $f\left(x\right)=0$