For the function $$ f(x)=\frac{\sqrt[7]{x}}{7} $$, find $$ f^{-1}(x) $$. Answer $$ f^{-1}(x)=(7 x)^{7} $$ $$ f^{-1}(x)=7 \sqrt[7]{x} $$ $$ f^{-1}(x)=\frac{x^{7}}{7} $$ $$ f^{-1}(x)=\left(\frac{x}{7}\right)^{7} $$

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Let $$ f(x)=\frac{\sqrt[7]{x}}{7} $$. To find $$ f^{-1}(x) $$, follow these steps:

1. Write the function with $$ y $$ instead of $$ f(x) $$:
   $$
   y=\frac{x^{\frac{1}{7}}}{7}
   $$

2. Swap the variables $$ x $$ and $$ y $$:
   $$
   x=\frac{y^{\frac{1}{7}}}{7}
   $$

3. Multiply both sides by 7 to isolate $$ y^{\frac{1}{7}} $$:
   $$
   7x=y^{\frac{1}{7}}
   $$

4. Raise both sides of the equation to the 7th power to solve for $$ y $$:
   $$
   (7x)^7=y
   $$

5. Therefore, the inverse function is:
   $$
   f^{-1}(x)=(7x)^7
   $$
$$ f^{-1}(x) = (7x)^7 $$

For the function , find .

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