1. **State the problem:** Find the inverse of the function $$g(x) = -3 + (x-1)^3$$. 2. **Recall the formula for inverse functions:** To find the inverse function $$g^{-1}(x)$$, we swap $$x$$ and $$y$$ in the equation and solve for $$y$$. 3. **Write the function with $$y$$:** $$y = -3 + (x-1)^3$$. 4. **Swap $$x$$ and $$y$$:** $$x = -3 + (y-1)^3$$. 5. **Isolate the cube term:** Add 3 to both sides: $$x + 3 = (y-1)^3$$ 6. **Take the cube root of both sides:** $$\sqrt[3]{x + 3} = y - 1$$ 7. **Solve for $$y$$:** $$y = 1 + \sqrt[3]{x + 3}$$ 8. **Write the inverse function:** $$g^{-1}(x) = 1 + \sqrt[3]{x + 3}$$ This is the inverse function of $$g(x)$$.