If the function $f:\left[2,\infty \right)\to \left[-1,\infty \right)$ is defined by $f\left(x\right)=x^2-4x+3$ then $f^{-1}\left(x\right)=$

• A

  $2-\sqrt{x+1}$

• B

  $2+\sqrt{x+1}$

• C

  $\frac{2-\sqrt{x+1}}{5}$

• D

  $\frac{2+\sqrt{x+1}}{5}$