Quiz 9

Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

1. Define f:\Bbb Z®\Bbb Z by f(x)=x+8.

(a) (3 pts.) Prove f is one-to-one.

(b) (3 pts.) Prove f is onto \Bbb Z.

(c) (1 pt.) Define g:\Bbb Z®\Bbb Z by g(x)=x²-1. Find g°f.

2. (3 pts.) Prove the following statement by induction.

(1- 1 4 )(1- 1 9 )...(1- 1 n2 )= n+1 2n

for all integers n ³ 2