Step 1 :Since \(g\) is the function that adds 13 and then divides by 11, \(g^{-1}\) is the function that multiplies by 11 and then subtracts 13. This lets us compute from inside out:
Step 2 :\(g^{-1}(g(-2))\) becomes \(g^{-1}(1)\) after substituting \(-2\) into \(g(x)\) and simplifying.
Step 3 :Then, \(g^{-1}(1)\) becomes \(11*1-13=\boxed{-2}\) after substituting \(1\) into \(g^{-1}(x)\) and simplifying.
Step 4 :\(h^{-1}(8)\) is the x-value such that \((x,8)\) is in the function \(h\). Looking at the definition of \(h\), we see that \(h^{-1}(8)=\boxed{7}\).