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.