Find the inverse function. $$ f(x)=x^{3}-13 $$ $$ \left.f^{-1}(x)=\sqrt[{[?}]\right]{x+\square} $$

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To find the inverse function of $$ f(x) = x^3 - 13 $$, follow these steps:

1. **Replace $$ f(x) $$ with $$ y $$:**
   $$
   y = x^3 - 13
   $$
   
2. **Solve for $$ x $$:**
   $$
   y + 13 = x^3
   $$
   $$
   x = \sqrt[3]{y + 13}
   $$
   
3. **Replace $$ y $$ with $$ f^{-1}(x) $$:**
   $$
   f^{-1}(x) = \sqrt[3]{x + 13}
   $$

So, the inverse function is:
$$
f^{-1}(x) = \sqrt[3]{\,x + 13\,}
$$
The inverse function is $$ f^{-1}(x) = \sqrt[3]{x + 13} $$.

Find the inverse function.

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