Dr. Sarah's Problem Set 2 on Functions

Please attach this sheet to your problem set solutions. Be sure to use the proof checklist


p. 23 #3

  • Prove that each of the following are functions.
  • For each function, provide a proof that it is one-one or a counterexample showing that it isn't.
  • Also provide a proof that the function is onto or a counterexample showing that it isn't.

    a) f(x)=x+3 from the reals into the reals

    b) f(x)=x^2+2x+1 from the reals into the reals

    c) f(x)=

    x if x is rational
    x^2 if x is irrational
    from the positive reals into the positive reals

     p. 24 #5.