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MATHS- Ten Functions Problems

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Question;Functions;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;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;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.

 

Paper#61090 | Written in 18-Jul-2015

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