Find the inverse function. $$ f(x)=x^{3}-7 $$ $$ f^{-1}(x)=[\sqrt[?]{x+[ }] $$

Question

UpStudy AI · Accepted Answer

To find the inverse function of $$ f(x) = x^3 - 7 $$, follow these steps:

1. **Start with the original function:**
   $$
   y = x^3 - 7
   $$

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   y + 7 = x^3
   $$
   $$
   x = \sqrt[3]{y + 7}
   $$

3. **Express the inverse function:**
   $$
   f^{-1}(x) = \sqrt[3]{x + 7}
   $$

So, the inverse function is:

$$
f^{-1}(x) = \sqrt[3]{\,x\;+\;7\,}
$$
The inverse function is $$ f^{-1}(x) = \sqrt[3]{x + 7} $$.

Find the inverse function.