Answer
Formula for the inverse $f^{-1}(x)=\sqrt[4] {(2-x)}$
The graph of the functions $f(x)=2-x^{4}$ and $f^{-1}(x)=\sqrt[4] {(2-x)}$
along the line $y=x$ on the same screen is depicted below:
Work Step by Step
Calculate the inverse of the function $f(x)=2-x^{4};x\geq0$
Write $y=f(x)$
$y=2-x^{4}$
Solve this equation for x in terms of y to get the inverse function.
$x=\sqrt[4] {(2-y)}$
To express $f^{-1}(x)$ as a function of x,interchange x and y. The resulting equation is
$y=\sqrt[4] {(2-x)}$
Therefore, the inverse of the function $f^{-1}(x)=y=\sqrt[4] {(2-x)}$
The graph of the functions $f(x)=2-x^{4}$ and $f^{-1}(x)=\sqrt[4] {(2-x)}$
along the line $y=x$ on the same screen is depicted below:
