NOTE: Be sure to read Homework
Format and Homework
Writing Policy BEFORE writing up your solutions to be turned in.
PROBLEMS WILL NOT BE GRADED AND NO CREDIT WILL BE GIVEN if these
guidelines are not followed.
But please don't copy lots of words onto your paper which are
irrelevant to understanding what the problems are asking you to do. Your
homework paper should contain information which is NECESSARY and SUFFICIENT
to understand what question you are answering without looking somewhere
else for this information.
Last modified Apr 21, 2008 10:07 AM
Due Wednesday, April 23
All functions considered below are assumed to have domain and codomain equal to the set of real numbers.
- Sect. 7:
- If you have already done Problem 6 correctly in Lesson 45a, you don't have to redo it; you have already received credit for it, as should be noted on your homework paper for Lesson 45 when it is returned.
- Redo Problem 6 in Lesson 45a.
Comment. This is not a “Math 323” level problem. It is a college algebra level problem. This problem involves understanding how to handle functions defined piecewise and to compute compositions. But the biggest issue is reading and following instructions carefully and using definitions carefully — in this case, the instructions which come with the specific definitions of the piecewise defined functions. (EVERY specific, explicitly given function comes with instructions: The instructions telling you how to determine an output for a given input.)
- More comment. Using definitions and following instructions is one big issue. The other big issue is recognizing that solving a math problem is not like putting meat in a meat grinder and turning the crank: In the latter case, the output may bear little similarity to the input, and you might have difficulty recognizing if a rat had gotten caught in the meat grinder and ground up with the meat. When solving a math problem, you should be able to think about your answer, see if and how it relates to the problem you were asked to solve, and see if it makes sense in terms of other things that you know.
In Problem 6 in Lesson 45a, a common answer was
(*) fog(x) = x for all real numbers x .
You start with the function f defined in Lessons 45 and 45a. You “prove” that there exists a function g which satisfies the equation just given. Answer the following questions:
- According to Exercise 7.32, what is such a function g called?
- According to Exercise 7.32, what property must the original f have in order for such a function g to exist?
- Does the original function f, as given in Lessons 45 and 45a, have this property?
- From Lessons 45 and 45a, we know that the function g we are discussing is a left inverse of the original f. Given this fact and the alleged equation (*) above, answer the following questions:
- According to Exercise 7.29(a), what property must the original f have in order for such a function g to exist?
- Does the original function f, as given in Lessons 45 and 45a, have this property?
- (New April 21.)
From your answers to the two preceding problems, and without knowing what the correct formula for fog is, can you tell whether the solution (*) is correct?
NOTE: Be sure to read Homework
Format and Homework
Writing Policy BEFORE writing up your solutions to be turned in.
PROBLEMS WILL NOT BE GRADED AND NO CREDIT WILL BE GIVEN if these
guidelines are not follows.
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 Apr 21, 2008 10:07 AM
Go to Lesson 46 (due April 14).
Go to Lesson 53 (due April 25).
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