Let $f(x)$ be the inverse function to the differentiable function $g(x).$ If $g(0)=1$ and $g^{\text{'}}(0)=3,$ find $f^{\text{'}}(1)$ :

$f^{\text{'}}(1)=3$

$f^{\text{'}}(1)=0$

There is not enough information to find $f^{\text{'}}(1).$

$f^{\text{'}}(1)=\frac{1}{3}$

$f^{\text{'}}(1)=-3$

$f^{\text{'}}(1)=-\frac{1}{3}$