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## Homework Statement

Given f(x) = x

^{2}+3x+2, what is f

^{-1}(f(x))?

## Homework Equations

## The Attempt at a Solution

Algebraically, getting f

^{-1}(x) is as follows:

y=x

^{2}+3x+2

x=y

^{2}+3x+2

y=+/-√(x+0.25)-1.5

f

^{-1}(x)=+/-√(x+0.25)-1.5

f

^{-1}(f(x))=+/-√(x

^{2}+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?