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Homework on 30 October 2019:

  1. [Not to be turned in]
    1. Prove that $f\colon\R\to\R$ by $f(x)=4x-1$ is a bijection.
    2. Prove that $f\colon{\R^2}\to{\R^2}$ by $f(x,y)=(x+2y,y-3x)$ is a bijection.
  2. [To be turned in on Friday]
    1. Find a function $f\colon\R\to\R$ that is one-to-one but not onto (and prove that it has the desired properties).
    2. Find a function $f\colon\R\to\R$ that is onto but not one-to-one (and prove that it has the desired properties).

    Note: Piecewise functions can be used. Be sure your functions are defined for all reals. Be careful about handling the for-all and there-exist statements involved.



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Created: 30 Oct 2019
Last modified: 30 Oct 2019 at 4:32 PM
Comments to: dpvc@union.edu
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