Last modified Mar 31, 2008 7:10 PM
NOTE: Be sure to read Homework Format and Homework Writing Policy BEFORE writing up your solutions to be turned in.
Due Monday, March 31
If you have previously solved 7.7(e) correctly, you can turn in the previous solution, provided that it is obvious what you are doing and what should be graded. But see Optional Hint below.Optional Hint. Think about the approach to Exercise 7.3(c), which follows Exercise 7.3(b).
- Sect. 7:
- 7.7(e)*.
* For 7.7(e), prove, using the standard method discussed in class for proving (or disproving) injective and surjective. Be sure to be complete; for example, if you claim that a function is injective but not surjective, explain or prove both assertions. As usual, use only simple algebra tools, not calculus or limits.
- Additional problem:
- Let g be the function defined by the same formula as the function f in Exercise 7.7(e), but with domain being the set of all real numbers. Repeat 7.7(e) for this function, and also find the image of the interval [0,1]. Prove your answers, using only simple algebra.
Added Mar 29: Take the codomain to be the set of real numbers.
NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.
Last modified Mar 31, 2008 7:10 PM
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Go to Lesson 38a.
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