# Inverse of a Function

## Homework Statement

Given f(x) = x2+3x+2, what is f-1(f(x))?

## 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?

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## Homework Statement

Given f(x) = x2+3x+2, what is f-1(f(x))?

## 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?
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.

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.
So does that mean the question is faulty since the inverse is not a function?