Find the inverse function of $$ f(x)=4+\sqrt[3]{x} $$ $$ f^{-1}(x)=\square $$

Question

UpStudy AI · Accepted Answer

Let $$ y = f(x) = 4 + \sqrt[3]{x} $$.

1. Subtract 4 from both sides:
   $$
   y - 4 = \sqrt[3]{x}
   $$

2. Cube both sides to eliminate the cube root:
   $$
   (y - 4)^3 = x
   $$

3. Swap $$ x $$ and $$ y $$ to find the inverse function:
   $$
   y = (x - 4)^3
   $$

Thus, the inverse function is:
$$
f^{-1}(x) = (x - 4)^3
$$
The inverse function is $$ f^{-1}(x) = (x - 4)^3 $$.

Find the inverse function of \( f(x)=4+\sqrt[3]{x} \) \( f^{-1}(x)=\square \)