Use algebra to find the inverse of the function $$ f(x)=-4 x^{7}+8 $$ The inverse function is $$ f^{-1}(x)=\square $$

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1. Begin with the function:
   $$
   y = -4x^7 + 8
   $$
2. Swap $$x$$ and $$y$$ to prepare for finding the inverse:
   $$
   x = -4y^7 + 8
   $$
3. Solve for $$y$$ by isolating the term containing $$y$$. First, subtract 8 from both sides:
   $$
   x - 8 = -4y^7
   $$
4. Divide both sides by $$-4$$:
   $$
   y^7 = \frac{8 - x}{4}
   $$
5. Take the seventh root of both sides to solve for $$y$$:
   $$
   y = \sqrt[7]{\frac{8 - x}{4}}
   $$
6. Thus, the inverse function is:
   $$
   f^{-1}(x) = \sqrt[7]{\frac{8 - x}{4}}
   $$
The inverse function is $$ f^{-1}(x) = \sqrt[7]{\frac{8 - x}{4}} $$.

Use algebra to find the inverse of the function \( f(x)=-4 x^{7}+8 \) The inverse function is \( f^{-1}(x)=\square \)

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