ฉันรักแปล - การแปลออนไลน์ - เว็บไซต์แปล - เครื่องมือการแปล - แปลข้อความ - แปลตามเนื้อความ - http://th.ilovetranslation.com/ะ 4G 9 18%18:02 พ. 11 ธ.ค.เสร็จสิ้นScanned Documents.pdf4g可0#0月5U#10Nx.9ONS2.2. IMAGES AND PREIMAGESis in f-I(f(X)). Let z e X. It muust be clear to you by now thatf(a) e f(X). Thus z is a part of all that maps into f(X). Putsymbolically, z e f-I(f(X)). We conclude that X c f-I(f(X)).All that maps to f(X)f-I(f(X))(2.8)Example 2.:2:7 Here are two examples of how f~'(f(X)) can begmuch larger than X.1. Consider the function f:R --- IR defned by f(r) = r2, andlet X = t2. A small calculation reveals that f(2) = 4. Thus2 E f-(4). The set f-l(4) is the set of allzt such that z2 = 4.A moment's thought will show you that f(2) = f(-2) = 4and that (-2,2 = f-'(4). Thus X = (2) # [-2,2 =f-'(f(X)).2. Let a : People on Earth -N be the function that assignsto each person z on Earth his/her age as of January 1, 2005.'Then a(your author) = 50 while a~'(50) is the set of all 50year olds on the planet. Hence a-'(a(your author)) = a~l(50)is quite a large set, not equal to just [your author).