If $f\left(x\right)=3x+10,g\left(x\right)=x^2-1$ , then ${\left(fog\right)}^{-1}$ is equal to

$=f\left(x^2-1\right)$

$=3\left(x^2-1\right)+10$

$=3x^2-3+10$

$=3x^2+7$

Let $fog\left(x\right)=y\Rightarrow x={\left(fog\right)}^{-1}\left(y\right)$

$3x^2+7=y$

$3x^2=y-7$

$x^2=\frac{y-7}{3}$

$x={\left(\frac{y-7}{3}\right)}^{\frac{1}{2}}$

${\left(fog\right)}^{-1}\left(y\right)={\left(\frac{y-7}{3}\right)}^{\frac{1}{2}}\Rightarrow {\left(fog\right)}^{-1}\left(x\right)={\left(\frac{x-7}{3}\right)}^{\frac{1}{2}}$