Let $f\left(x\right)=x^3+1$ and let $g\left(x\right)=f^{-1}\left(x\right)$ then the reciprocal of $g\text{'}\left(28\right)$ is equal to 

The given function is $f\left(x\right)=x^3+1$

$g\left(x\right)=f^{-1}\left(x\right)={\left(x-1\right)}^{\frac{1}{3}}$

$g\text{'}\left(x\right)=\frac{1}{3}{x}^{-\frac{2}{3}}$

$g^1\left(28\right)=\frac{1}{3}{\left(27\right)}^{-\frac{2}{3}}=\frac{1}{27}$

Therefore, the reciprocal of $g\text{'}\left(28\right)$ is $27$