Find the inverse function. $$ f(x)=x^{3}-14 $$ $$ \left.f^{-1}(x)=\sqrt[{[?}]\right]{x+\square} $$

Question

UpStudy AI · Accepted Answer

To find the inverse function $$ f^{-1}(x) $$ of the function $$ f(x) = x^3 - 14 $$, follow these steps:

1. **Start with the original function:**
   $$
   y = x^3 - 14
   $$

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   y + 14 = x^3
   $$
   $$
   x = \sqrt[3]{y + 14}
   $$

3. **Express the inverse function:**
   $$
   f^{-1}(x) = \sqrt[3]{x + 14}
   $$

So, the inverse function is:
$$
f^{-1}(x) = \sqrt[3]{x + 14}
$$

In the given format:
$$
f^{-1}(x) = \sqrt[{3}]{x + 14}
$$

**Answer:**
$$
f^{-1}(x) = \sqrt[3]{\,x\ +\ 14\,}
$$
The inverse function is $$ f^{-1}(x) = \sqrt[3]{x + 14} $$.

Find the inverse function. \( f(x)=x^{3}-14 \) \( \left.f^{-1}(x)=\sqrt[{[?}]\right]{x+\square} \)