The discussion centers on finding the inverse of the function f(x) = x² + 3x + 2 and determining f-1(f(x)). The derived inverse function is f-1(x) = ±√(x + 0.25) - 1.5, leading to f-1(f(x)) = ±√(x² + 3x + 2 + 0.25) - 1.5. The conclusion is that f-1(f(x)) results in either x or -x - 3, but the function f(x) does not have a true inverse because it is not one-to-one, as indicated by the ± symbol in the inverse function.
PREREQUISITESStudents studying algebra, particularly those focusing on functions and their inverses, as well as educators seeking to clarify the concept of one-to-one functions.
kris2fer said:Homework Statement
Given f(x) = x2+3x+2, what is f-1(f(x))?
Homework Equations
The Attempt at a Solution
Algebraically, getting f-1(x) is as follows:
y=x2+3x+2
x=y2+3x+2
y=+/-√(x+0.25)-1.5
f-1(x)=+/-√(x+0.25)-1.5
f-1(f(x))=+/-√(x2+3x+2+0.25)-1.5
f-1(f(x))=+/-√(x+1.5)2-1.5
f-1(f(x))=x or -x-3
I thought f-1(f(x)) was always x. What's wrong with -x-3?
Dick said:Yes, it's always x. Your function doesn't even have an inverse, it's not 1-1. As the +/- is telling you. That's what's going wrong.