[tex]\boxed{\boxed{f^{-1}(x)=\sqrt[5]{\frac{x+2}{5}}}}[/tex]
The inverse function is formed by interchanging the first and second coordinates of each ordered pairs of a function. To find the inverse of the function:
[tex]f(x)=5x^5-2[/tex]
Let's follow these steps:
1. Use the Horizontal Line Test to figure out whether the function has an inverse or not.
From the First graph, we see that any horizontal line passes through the graph of our function in just one point. So this function has an inverse.
2. Replace [tex]f(x)[/tex] by [tex]y[/tex]:
[tex]y=5x^5-2[/tex]
3. Interchange [tex]x \ and \ y[/tex]:
[tex]x=5y^5-2[/tex]
4. Solve for [tex]y[/tex]:
[tex]x=5y^5-2 \\ \\ x+2=5y^5 \\ \\ y^5=\frac{x+2}{5} \\ \\ y=\sqrt[5]{\frac{x+2}{5}}[/tex]
5. Replace [tex]y \ by \ f^{-1}(x)[/tex]:
[tex]f^{-1}(x)=\sqrt[5]{\frac{x+2}{5}}[/tex]
Symmetry for inverse functions: https://brainly.com/question/12253822
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