What is the inverse of $$ f(x)=2 \sqrt[3]{x-3} $$ ? (1 point) $$ f^{-1}(x)=\left(\frac{x}{2}-3\right)^{3} $$ $$ f^{-1}(x)=\left(\frac{x}{2}\right)^{3}+3 $$ $$ f^{-1}(x)=\left(\frac{x}{2}+3\right)^{3} $$ $$ f^{-1}(x)=\left(\frac{x}{2}\right)^{3}-3 $$

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To find the inverse of the function $$ f(x) = 2 \sqrt[3]{x - 3} $$, follow these steps:

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

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   \frac{y}{2} = \sqrt[3]{x - 3}
   $$
   $$
   \left(\frac{y}{2}\right)^3 = x - 3
   $$
   $$
   x = \left(\frac{y}{2}\right)^3 + 3
   $$

3. **Express the inverse function $$ f^{-1}(x) $$:**
   $$
   f^{-1}(x) = \left(\frac{x}{2}\right)^3 + 3
   $$

**Answer:**
$$ f^{-1}(x)=\left(\frac{x}{2}\right)^{3}+3 $$
The inverse function is $$ f^{-1}(x)=\left(\frac{x}{2}\right)^{3}+3 $$.

What is the inverse of ? (1 point)

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