Find the Inverse of a Function: f-1(f(x)) = +/-√(x+0.25)-1.5

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The discussion revolves around finding the inverse of the function f(x) = x² + 3x + 2. The calculated inverse, f⁻¹(x) = ±√(x + 0.25) - 1.5, indicates that the function is not one-to-one due to the presence of the ± sign. Consequently, f⁻¹(f(x)) results in two potential outputs: x or -x - 3. This leads to the conclusion that f⁻¹(f(x)) is not always equal to x, as the original function lacks a proper inverse. The question is deemed faulty since the inverse does not qualify as a function.
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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?
 
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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?

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.
 
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.

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

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