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Download Solution for Assignment 4 - Introduction to Mathematical Reasoning | MATH 310 and more Assignments Mathematics in PDF only on Docsity!
Math 310 Assignment 4 PROBLEMS: 3.41, 4.6, 4.10, 4.12, 4.24, 4.25, 4.96, 4.34, 4.45, 5.6 In addition, complete the following supplemental problem (don't recopy the table, simply fill it in and staple this sheet to your HW): PROBLEM I: Put an ‘T’ in each entry in the table that is TRUE (No proofs required). Assume the domains and targets for the functions labeled with f, g, hy and he are as follows: f:R SR, g:R-{O} 3R, mh: (-8, 8) — R, and hg: R-{a:a=*keZ}R. Note that the domains and targets given will effect whether the function is injective, surjective, or monotone. FUNCTION INJECTIVE? | SURJECTIVE? | BIJECTIVE? | MONOTONE? f@j=5 pA f(zj)=ar4+1 x x x x f@=2 faj= x x > flaj)=a'—3z pra f(z) = e* fx xX f(z) = sin(z) f(x) = arctan(z) ~*~ x gz) = Ve x fy(a) = tan(z) x bas [8 ~*~ ha(a) = tan(z) x T hope that this table helps you better understand these terms and helps you come up with counterex- amples on the rest of the homework. PROBLEM II: Prove that if f : R + Rand g : R — R are both decreasing, then h = go f is increasing. (this is not a typo!) The problems above are DUE FRIDAY, OCTOBER 31 at lecture or by 3:00pm at my office. This is a challenging assignment (especially if you are new to the terms: one-to-one, onto, bijection, and monotone), so start early and visit my office hours. I am available for the 45 minutes before and 30 minutes after class in the Paul G. Allen lobby and from 2:40-3:40 MW (and most Fridays) in my office (Padelford C-339). You can also email me quick clarifying questions and I am happy to answer what | ean via email. 
