Hi, need some help in the aspect of finding the inverse of a quadratic function. I know how to solve simple ones, but what happens when the quadratic function is in the form of a fraction
f(x) = (x^2 - x + 1) / (x^2 + x + 1)
So far I have only gotten this far:
y = (x^2 - x + 1) / (x^2 + x + 1)
yx^2 + yx + y = x^2 - x + 1
(y-1)x^2 + (y+1)x + (y-1) = 0
(y-1)(x^2 +1) + (y+1)x = 0
Thanks in advance!
Notice that because f(x) is not a one-to-one function, there are zero, one, or two solutions for a given y, so there is no single inverse function.
This is a quadratic equation in x, and now you can apply the quadratic formula.