DEFINITION 1 函数 122函数 Functions / Mapping映射
F u n c t i o n s 函 数 DEFINITION 1. 1.2.2 函数 Functions /Mapping 映射
DEFINITION 1 函数 Let a and b be sets. a function f from a to b is an assignment of exactly one element of b to each element ofA. We write f(a)=b if b is the unique element of B assigned by the function f to the element a ofA. If f is a function from A to B. we write f:A-B
F u n c t i o n s 函 数 DEFINITION 1. Let A and B be sets. A function f from A to B is an assignment of exactly one element of B to each element of A. We write f(a) = b if b is the unique element of B assigned by the function f to the element a of A. If f is a function from A to B, we write f : A→B
DEFINITIONZ 函数 If f is a function from A to b, we say that a is the domain of f and B is the codomain of f. If f(a)=b, we say that b is the image of a and a is a pre-image of b. The range of f is the set of all images of elements of A. Also, if f is a function from A to B, we say that f maps a to B A:定义域/ domain of f a:b的原象/pre-mage B:陪域/ codomain of f b:a的象/ mage f(A):值域/ range of f
F u n c t i o n s 函 数 DEFINITION 2. If f is a function from A to B, we say that A is the domain of f and B is the codomain of f. If f (a) = b , we say that b is the image of a and a is a pre-image of b. The range of f is the set of all images of elements of A. Also, if f is a function from A to B, we say that f maps A to B. A：定义域/domain of f a: b 的原象/pre-image B：陪域/codomain of f b: a的象/image f（A）：值域/range of f
DEFINTION3 函数 当B= Real set Let f and f be function from a to r Then f,+f and f, f, are also functions from a to r defined by (f1+f2)(x)=f1(x)+f2(x) (f1f2)(x)=f1(x)f2(x)
F u n c t i o n s 函 数 DEFINITION 3. Let f1 and f2 be function from A to R. Then f1 + f2 and f1 f2 are also functions from A to R defined by (f1 + f2 )(x) = f1 (x) + f2 (x), (f1 f2 )(x) = f1 (x) f2 (x). 当B=Real Set
DEFINITION 4 函数 Let f be a function from the set a to the set b and let s be a subset of A. The image of s is the subset ofb that consists of the images of the elements ofs. We denote the image ofs by f(S), so that f(S)={f(s)|s∈S} A的子集S的象
F u n c t i o n s 函 数 DEFINITION 4. Let f be a function from the set A to the set B and let S be a subset of A. The image of S is the subset of B that consists of the images of the elements of S. We denote the image of S by f (S), so that f (S) = { f (s)∣s∈S}. A的子集S的象
DEFINITION 1 函数 Let f be a function from the set a to the set B. The graph of the function f is the set of ordered pairs((a, b)|a∈ Aand f(a)=b}
F u n c t i o n s 函 数 DEFINITION 11. Let f be a function from the set A to the set B. The graph of the function f is the set of ordered pairs {(a, b)∣a∈A and f (a) = b}
EXAMPLE 20 函数 Display the graph of the function f(x)=xfrom the set of integers to the set of integers
F u n c t i o n s 函 数 EXAMPLE 20 Display the graph of the function f(x) = x2 from the set of integers to the set of integers
DEFINITION 1 函数 函数的分类
F u n c t i o n s 函 数 DEFINITION 1. 函数的分类
DEFINITIONS 函数 A function f is said to be one-to-one, or injective, if and only f(x)=f(y) implies that x=y for all x and y in the domain of. A function is said to be an injection if it is one-to-one 对一,单函数,单射
F u n c t i o n s 函 数 DEFINITION 5. A function f is said to be one-to-one, or injective, if and only f (x) = f (y) implies that x = y for all x and y in the domain of f. A function is said to be an injection if it is one-to-one. 一对一，单函数，单射
EKAMPLE G 函数 Determine whether the function f from a, b, c, d to(1, 2, 3, 4, 5) with f(a)=4,f(b)=5,f(Cc)=1,andf(d)=3 is one-to-one
F u n c t i o n s 函 数 EXAMPLE 6 Determine whether the function f from {a, b, c, d} to (1, 2, 3, 4, 5) with f(a) = 4, f(b) = 5, f(c) = 1, and f(d) = 3 is one-to-one