Question

The range of $f\left(x\right)=\frac{\sin \pi [x^2-1]}{x^4+1}$ is

• A. $R$
• B. $[-1,1]$
• C. $\{0,1\}$
• D. $\left\{0\right\}$

Answer 1

The correct option is D $\left\{0\right\}$

$f\left(x\right)=\frac{\sin \pi [x^2-1]}{x^4+1}$
$\because [x^2-1]$ will always give an integer for any value of $x$
So, $\sin \pi [x^2-1]=\sin \pi$
$=0$
Hence, option 'D' is correct.