PDF HW7 S16-corrected pdf x C https:// drive.google.com You are certifying that

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PDF HW7 S16-corrected pdf x C https:// drive.google.com You are certifying that all work follows the homework policy for collaboration, allowed sources, etc Write legibly Write explanations of your responses for full credit: 3/8th credit is writing score Write name on and staple all pages. No jagged edges from spiral bound paper 4 bonus points awarded for each non-trivial error reported 48 hours before the deadline 1. Consider the function f {n E Z 6 s n s 6) Z defined by f (n3 5n -1) /5 Note that the domain of f is finite (a) Write down the domain as a set with every element listed explicitly. Write down the set description of the f. Write down the Cartesian product that the set description of f is a subset of (You may use a computer or calculator to compute the various f(n).) (b) Write down the set f 1, the "reverse" of the function. What Cartesian product is f-1 a subset of? (c) Find a as small as possible so that restricting f to domain In E Z a S n S 6 results in a one-to-one function (d) Find b as large as possible so that restricting f to domain {n E Z 6 S n S b results in a one-to-one function (e) Remove as few domain elements from the middle of In E Z 6 S n S 6 as possible to obtain a subset A C {n E Z 6 S n S 6 so that the new restricted function g A Z is one-to-one (The new domain will exclude a elements of the form {c 1 d -1 with -6 c d 6.) (f) Is the function g A+ z that you computed in Part (e) onto (surjective)? If not, find a new target B and a function h A B hat does the same thing as g, except on the smaller target B (g) Note that h is invertible because it is one-to-one and onto. Compute the inverse function of h and be sure to identify the three defining features of h: the domain, the target, and the rule (either an arrow diagram or set description suffice for defining the rule 2. Prove or disprove. For all real numbers z and y, La tr y LaJ LyJ e., the floor function distributes over addition for the reals En a OK 0.1 10:31 4) ENG 2016/3/1

Explanation / Answer

1 a) Domain - { -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

f = { -38, -21, -9, -3, 0,0, -1, -1, -1, 2, 8, 19, 37}

c) From the above, if we set a = 2, we get a one on one function in f

d) b = -2

e) Remove the 2nd instance of 0 and 2 instances of -1

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