The problem involves finding a function f(x) such that f(f(x) - x²) = x² - 5x + 3. The subject area pertains to composite functions and polynomial functions.
The discussion is ongoing, with participants exploring different assumptions about the nature of f(x). Some guidance has been offered regarding the potential forms of f(x) and the relationship between the degrees of the functions involved.
There is a repeated emphasis on the polynomial nature of f(x) and the exploration of its degree in relation to the composite function. Participants are considering the implications of these assumptions without reaching a definitive conclusion.
It seems reasonable to assume that f(x) is a polynomial.songoku said:Homework Statement
Find f(x) given that f ( f(x) - x2) = x2 - 5x + 3
Homework Equations
Not sure
The Attempt at a Solution
I tried assuming f(x) = ax + b and use composite function but end up wrong. Please give me idea to start
Thanks
SammyS said:It seems reasonable to assume that f(x) is a polynomial.
If you compose linear function and a quadratic you get a quadratic function.
One way to do that is for f(x) to be linear, which is what you tried & you say doesn't work.
Another way is for f(x) to be a quadratic such that f(x) - x2 is linear.
Try that.