If $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{ll}\frac{\sqrt{\mathrm{g}\left(\mathrm{x}\right)}–1}{\sqrt{\mathrm{x}}–1};& \mathrm{x}\ne 1\\ 1;& \mathrm{x}=1\end{array}\right.$ and ${\mathrm{g}}^{\text{'}}\left(1\right)=2,\mathrm{ }\mathrm{g}\left(1\right)=1$, then $\underset{\mathrm{x}\to 1}{\lim }\mathrm{f}\left(\mathrm{x}\right)$ is equal to

• A

  $1$
• B

  $3$
• Correct answer
  C

  $2$
• D

  $4$

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