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MATHS- Ten Functions Problems

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Subject: Mathematics
Due on: 03/31/2014
Posted On: 03/22/2014 10:29 AM

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Functions

  1. Let A = {q, r, s, t} and B = {17, 18, 19, 20}. Determine which of the following are functions. Explain why or why not.

2. Give the ranges of each of these functions where sets A and B are as stated in #1:

    1. }

3. State whether each of these functions, where sets A and B are as stated in #1, are one-to-one, onto, both, or neither, and give a brief explanation for each answer:

    1. }

4. Determine all bijections from A into B.

a. A = {q, r, s} and B = {2, 3, 4}

b. A = {1, 2, 3, 4} and B = {5, 6, 7, 8}

5. Which of the following functions fromare one-to-one, onto, or both? Prove your answers.

a.

b.

c.

d.

e.

6. For each function in parts a through f, state a domain that, if it was the domain of the given function, would make the function one-to-one, and explain your answer. If no such domain exists, explain why not. (Hint: graph the function and use the appropriate line test).

a.

b.

c.

d.

e.

f. |

7. For each function in parts a through f, state a codomain that, if it was the codomain of the given function, would make the function onto, and explain your answer. If no such codomain exists, explain why not.

a.

b.

c.

d.

e.

f. |

8. Let f= {(-2, 3), (-1, 1), (0, 0), (1, -1), (2, -3)} and

let g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)}. Find:

a. f(1)

b. g(-1)

c.

d.

e.

9. Define q, r, and s, all functions on the integers, by,, and. Determine:

a.

b.

c.

d.

10. Consider the functions f, g (both on the reals) defined byand.

a. Show that fis injective.

b. Show that f is surjective.

c. Find.

d. Find.

e. Find.

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MATHS- Ten Functions Problems

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Preview: r, xx s, xx t, t}Determine xxx bijections from x into x x = xxx r, s} xxx B = xxx 3, xxx x {1, xx 3, 4} xxx B = xxx 6, xx xxxxxxx of xxx following functions xxxx R?R are xxxxxxxxxxx onto, xx xxxxx Prove xxxx answers fx=3x-4gx= xxxxxxx 2xkx=ln?(x)lx=exFor each xxxxxxxx in xxxxx x through xx state a xxxxxx that, if xx was xxx xxxxxx of xxx given function, xxxxx make the xxxxxxxx one-to-one, xxx xxxxxxx your xxxxxx If no xxxx domain exists, xxxxxxx.....
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