Each question is worth 7 points
Time allowed is 4 hours
No books, notes or calculators permitted
Write full proofs with your answers
1) Find all real numbers such that there are four different real numbers satisfying the equation
2) Find all functions such that for we have
3) Suppose that , and are real numbers satisfying the following three equations.
Find all possible values of .
4) Suppose that a function has the property that
for every .
Prove that for all .
5) Prove the following inequality for all .