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I'm interested in looking at mappings of functions.

For example, how would I come up with a function $f:x\in[0,\infty)|\longmapsto\ (-\infty, 0]$ where $f(x)=x^2.$ Basically I want to glue every point to the right of this function to the left.

GA316
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Mr.Fry
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  • If I've understood the question correctly, no such function exists. Basically, the graph of any such function would be a subset of $[0,\infty) \times (-\infty,0],$ which is the bottom-right quadrant of the Cartesian plane. However, the graph of $x^2,$ viewed as a subset of $\mathbb{R}^2$, remains outside this quadrant, except at $(0,0)$. Therefore, no such function exists. – goblin GONE Nov 07 '13 at 06:46
  • Yes, this is true. I should of thought about this before asking, but thanks. – Mr.Fry Nov 07 '13 at 06:47
  • Your welcome! $\!\!$ – goblin GONE Nov 07 '13 at 06:50

1 Answers1

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HINT: Construct a function mapping positive elements to their additive inverse. This is impossible with $f(x) = x^2$.

Don Larynx
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