$f(x)$ is a quadratic polynomial satisfying the condition $f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right)$. If $f(-1)=0$, then the range of $f$ is

• A

  $[1, \infty)$
• B

  $[-1,1]$
• Correct answer
  C

  $(-\infty, 1]$
• D

  $\mathbb{R}$

Hence, the correct answer is option: 'C'.