How to find the formula for the inverse of the following function?
f(x)=2x^2-x^4 defined on x in [0,1]
1 Answer
Mar 5, 2018
Explanation:
Given:
f(x) = 2x^2-x^4" " on" "[0, 1]
Let
0 = x^4-2x^2+y
color(white)(0) = x^4-2x^2+1+y-1
color(white)(0) = (x^2-1)^2+y-1
Hence:
(x^2-1)^2 = 1 - y
Note that
So:
x^2-1 = -sqrt(1-y)
Add
x^2 = 1-sqrt(1-y)
Take the positive square root (since
x = sqrt(1-sqrt(1-y))
So:
f^(-1)(y) = sqrt(1-sqrt(1-y))