{ "key_pair_value_system": true, "answer_rating_count": "", "question_feedback_html": { "html_star": "", "html_star_feedback": "" }, "answer_average_rating_value": "", "answer_date_js": "2024-06-08T14:03:09-04:00", "answer_date": "2024-06-08 14:03:09", "is_docs_available": "", "is_excel_available": "", "is_pdf_available": "", "count_file_available": 0, "main_page": "student_question_view", "question_id": "2477839", "url": "\/study-help\/questions\/l42-inverse-images-of-sets-we-just-showed-that-a-2477839", "question_creation_date_js": "2024-06-08T14:03:09-04:00", "question_creation_date": "Jun 08, 2024 02:03 PM", "meta_title": "[Solved] l.4.2 Inverse images of sets We just show | SolutionInn", "meta_description": "Answer of - l.4.2 Inverse images of sets We just showed that a function f 1 A r B \\pushes formrd subsets of A to subsets of B.\\ We | SolutionInn", "meta_keywords": "l.4.2,inverse,images,sets,showed,function,1,pushes,formrd,subsets,pull,back", "question_title_h1": "l.4.2 Inverse images of sets We just showed that a function f 1 A r B pushes formrd subsets of A to subsets of B.", "question_title": "l.4.2 Inverse images of sets We just showed that a function f", "question_title_for_js_snippet": "l 4 2 Inverse images of sets We just showed that a function f 1 A r B pushes formrd subsets of A to subsets of B We can also pull back subsets of 3 DEFINITION 6 If is a subset of B, we dene f T a e A f(a) E T The set f'l T is a subset of A and is called the inverse image of T under f or the pie image of T under f Just as with images there are two ways to think about inverse images ' One interpretation involves a test condition on elements ofthe domain A To nd f' l T , we check each element a of A We compute f (a) and check whether it is an element of T If it is, we include it in f T If it's not, we don't Here is a second interpretation To compute f T , we run through each element 1 e T We compute a e A a) t (This is exactly f l l , the inverse image of a set containing a single point ) We collect the Inverse images the collection of all elements obtained by this process (running through all elements I e T) is exactly f T Symbolieally, we have that f T Ure'r f'llllll 1 Carefully explain how you can find f 1 (5, 4, 0, 1 and f ' 4, 9 from the graph of f (x) x2, where the domain of f is taken to be R (This exercise should help reinforce what you learned in Your Turns 12 and 13 )", "question_description": "\"image\"image
\"image\"image<\/div><\/div><\/div><\/figure> l.4.2 Inverse images of sets We just showed that a function f 1 A r B \\\"pushes formrd subsets of A to subsets of B.\\\" We can also \\\"pull back subsets of 3\\\": DEFINITION 6. If?\" is a subset of B, we dene f\"[T] = {a e A :f(a) E T]. The set f'l[T] is a subset of A and is called the inverse image of T under f or the pie-image of T under f. Just as with images. there are two ways to think about inverse images: ' One interpretation involves a test condition on elements ofthe domain A. To nd f'\\\"l [T], we check each element a of A. We compute f (a) and check whether it is an element of T. If it is, we include it in f\\\" [T]. If it's not, we don't. - Here is a second interpretation. To compute f\"[T], we run through each element 1 e T. We compute [a e A : a) : t}. (This is exactly f\"[l!l], the inverse image of a set containing a single point.) We collect the Inverse images; the collection of all elements obtained by this process (running through all elements I e T) is exactly f \"[T]. Symbolieally, we have that f \\\"[T] = Ure'r f'llllll- 1. Carefully explain how you can find f-1[(5, 4, 0, -1}] and f-'[[4, 9]] from the graph of f (x) = x2, where the domain of f is taken to be R. (This exercise should help reinforce what you learned in Your Turns 12 and 13.)", "transcribed_text": "", "related_book": { "title": "College Algebra", "isbn": "134697022, 9780134313795 , 978-0134697024", "edition": "12th edition", "authors": "Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels", "cover_image": "https:\/\/dsd5zvtm8ll6.cloudfront.net\/si.question.images\/book_images\/1812.jpg", "uri": "\/textbooks\/college-algebra-12th-edition-1812", "see_more_uri": "" }, "free_related_book": { "isbn": "0128125225", "uri": "\/textbooks\/advances-in-molecular-toxicology-vol-11-1st-edition-9780128125229-9780128125236", "name": "Advances In Molecular Toxicology Vol 11", "edition": "1st Edition" }, "question_posted": "2024-06-08 14:03:09", "see_more_questions_link": "\/study-help\/questions\/sciences-biology-2023-February-20", "step_by_step_answer": "The Answer is in the image, click to view ...", "students_also_viewed": [ { "url": "\/turco-products-uses-a-job-order-cost-system-the-following", "description": "Turco Products uses a job order cost system. 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