If the range of the real valued function $f(x)=\frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$, then $k=$

• A

  2
• B

  -2
• Correct answer
  C

  1
• D

  2

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