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

[kris2fer]

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]

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.

 

[kris2fer]

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?