SOLUTION:
We are to find the inverse of the given function;
[tex]\begin{gathered} y\text{ = -4 }\sqrt[]{x}\text{ -1} \\ y\text{ +1 = -4 }\sqrt[]{x} \\ \sqrt[]{x\text{ }}\text{ = }\frac{y\text{ + 1}}{-4} \\ \\ x\text{ = }\frac{(y+1)^2}{(-4)^2} \\ \\ x\text{ }=\text{ }\frac{(y+1)^2}{16^{}} \\ \\ f^{-1}(x)\text{ = }\frac{(x+1)^2}{16^{}}\text{ , x }\leq\text{ -1} \end{gathered}[/tex]
