Deck 7: Functions

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

a. Proof that g is one-to-one: Suppose x1 and x2 are any nonzero real numbers and
g(x1) = g(x2). [We must show that x1 = x2.]
By definition of g,
Proof that g is onto: Let y be any nonzero real number. [We must show that there is a
nonzero real number whose image under g is y.]

Question 4

Let f be a function from a set X to a set Y. Define precisely (but concisely) what it means for
f to be onto.

Question 5

Fill in the blanks:
because .

Question 6

Question 7

Question 8

Is
Why or why not?

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

(a) Draw an arrow diagram for a function that is onto but not one-to-one.
(b) Draw an arrow diagram for a function that is one-to-one but not onto.

Question 15

Question 16

Question 17

Let f be a function from a set X to a set Y. Define precisely (but concisely) what it means for
f to be one-to-one.

Question 18

Question 19

Question 20

Question 21

Prove that the set of all integers and the set of all odd integers have the same cardinality.