Use algebra to find the inverse of the function $$ f(x)=5 x^{5}+4 $$ The inverse function is $$ f^{-1}(x)= $$

Question

UpStudy AI · Accepted Answer

Let $$ y = 5x^5 + 4 $$.

1. **Swap $$ x $$ and $$ y $$:**

$$
   x = 5y^5 + 4
   $$

2. **Solve for $$ y $$:**

- Subtract 4 from both sides:

$$
     x - 4 = 5y^5
     $$

- Divide both sides by 5:

$$
     y^5 = \frac{x-4}{5}
     $$

- Take the fifth root of both sides:

$$
     y = \sqrt[5]{\frac{x-4}{5}}
     $$

3. **Write the inverse function:**

$$
   f^{-1}(x) = \sqrt[5]{\frac{x-4}{5}}
   $$
The inverse function is $$ f^{-1}(x) = \sqrt[5]{\frac{x-4}{5}} $$.

Use algebra to find the inverse of the function \( f(x)=5 x^{5}+4 \) The inverse function is \( f^{-1}(x)= \)