Uncovering the Mystery of Graph 2: Analysis & Explanation

[temaire]

Homework Statement

http://img220.imageshack.us/img220/2813/graphmo4.jpg​

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Homework Equations

Not necessary

The Attempt at a Solution

The answers that I have up there are correct, but I was wondering why graph 2 did not look something like this:
http://img218.imageshack.us/img218/256/graph2rx8.jpg

 

[rock.freak667]

Let y=x^2 so x=sqrt(y)

so $f^{-1}(x)=\sqrt{x}$ and $f^{-1}(f(x))=\sqrt{x^2}$

 

[Tedjn]

In fact, the inverse of $y=x^2$ is $y=\sqrt{x}, x \geq 0$ and $y=-\sqrt{x}, x < 0$. It doesn't matter in the end, however, because the definition of an inverse says that $f^-1(f(x)) = x$

 

[HallsofIvy]

Actually, that's a seriously bad question! Since y= x² is not one-to-one, it does not have an inverse! temaire, the graph you showed would be the "inverse function" to x² but, as you can see from the graph, there are two values of x for each positive y and so it is not a function.,