33 Multiple Choice 1 point Which function is the inverse of $$ g(x)=x^{3}+11 $$ ?

Question

UpStudy AI · Accepted Answer

To find the inverse of the function $$ g(x) = x^3 + 11 $$, follow these steps:

1. **Replace $$ g(x) $$ with $$ y $$:**
   $$
   y = x^3 + 11
   $$

2. **Solve for $$ x $$:**
   $$
   y - 11 = x^3
   $$
   $$
   x = \sqrt[3]{y - 11}
   $$

3. **Express the inverse function:**
   $$
   g^{-1}(x) = \sqrt[3]{x - 11}
   $$

**Final Answer:**
$$
g^{-1}(x) = \sqrt[3]{\,x\ -\ 11\,}
$$
The inverse function is $$ g^{-1}(x) = \sqrt[3]{x - 11} $$.

33 Multiple Choice 1 point Which function is the inverse of \( g(x)=x^{3}+11 \) ?