Find the inverse function. $$ f(x)=x^{3}-18 $$ $$ \left.f^{-1}(x)=\sqrt[{[?}]\right]{x+\square} $$

Question

UpStudy AI · Accepted Answer

To find the inverse function of $$ f(x) = x^3 - 18 $$, follow these steps:

1. **Express $$ y $$ in terms of $$ x $$:**
   $$
   y = x^3 - 18
   $$

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   y + 18 = x^3
   $$
   $$
   x = \sqrt[3]{y + 18}
   $$

3. **Replace $$ y $$ with $$ x $$ to get the inverse function:**
   $$
   f^{-1}(x) = \sqrt[3]{x + 18}
   $$

So, the inverse function is:

$$
f^{-1}(x) = \sqrt[3]{\, x\ +\ 18\,}
$$
The inverse function is $$ f^{-1}(x) = \sqrt[3]{x + 18} $$.

Find the inverse function.