Arrow diagram.<\/li>\n<\/ol>\nUniversal relation from A to B is A \u00d7 B.<\/p>\n
Empty relation from A to B is empty set \u03c6.<\/p>\n
A relation in A is a subset of A \u00d7 A.<\/p>\n
The number of relation that can be written from A to B if n(A) = p, n(B) = q is 2pq.<\/p>\n
Domain: It is the set of all first elements of the ordered pairs in a relation.<\/p>\n
Range: It is the set of all second elements of the ordered pairs in a relation. \nIf R: A \u2192 B, then R(R) \u2286 B.<\/p>\n
Co-domain: If R: A \u2192 B, then Co-domain of R = B.<\/p>\n
III. Functions:<\/span> \nA relation f from A to B (f : A \u2192 B) is said to be a function if every element of set A has one and only one image in set B.<\/p>\nIf f : A \u2192 B is a function defined by f(x) = y.<\/p>\n
\nThe image of x = y<\/li>\n The pre-image of y = x<\/li>\n Domain of f = {x \u2208 A : f(x) \u2208 B}<\/li>\n Range of f = {f(x) : x \u2208 D(f)}<\/li>\n If f : A \u2192 B, then n(f) = n(B)n(A)<\/li>\n<\/ol>\nIV. Some Important Functions<\/span><\/p>\nIdentity function: A function f : R \u2192 R defined by f(x) = x. Here D(f) = R, R(f) = R. \nThe graph of the above function is a straight line passing through the origin which makes 45 degrees with the positive direction of the x-axis.<\/p>\n
Constant function: A function f : R \u2192 R defined by f(x) = c, where c is a constant. \nHere D(f ) = R, R(f) = {c}. \nThe graph of the above function is a straight line parallel to the x-axis.<\/p>\n
Polynomial function: A function f : R \u2192 R defined by \nf(x) = a0<\/sub> + a1<\/sub>x + ….. + an<\/sub>xn<\/sup>, where n is a no-negative integer and a0<\/sub>, a1<\/sub>, …., an<\/sub> \u2208 R.<\/p>\nRational function: A function f: R \u2192 R defined by \\(f(x)=\\frac{p(x)}{q(x)}\\), where p(x), q(x) are functions of x defined in a domain, where q(x) \u2260 0<\/p>\n
Modulus function: A function f: R \u2192 R \n \nHere D(f) = R, R(f) = [0, \u221e). \nThe graph of the above function is \u2018V\u2019 shaped with a corner at the origin.<\/p>\n
Signum function: A function f: R \u2192 R \n \nHere D(f) = R, R(f) = {-1, 0, 1}. \nThe graph of the above function has a break at x = 0.<\/p>\n
Greatest integer function f: R \u2192 R defined by \n \nHere D(f) = R, R(f) = Z. \nThe graph of the above function has broken at all integral points.<\/p>\n
V. Algebra of Functions<\/span><\/p>\nLet f : X \u2192 R and g : X \u2192 R be any two real functions, where X \u2282 R. Then, we define (f + g) : X \u2192 R by (f + g)(x) = f(x) + g(x) for all x \u2208 X<\/p>\n
Let f : X \u2192 R and g : X \u2192 R be any two real functions, where X \u2282 R. Then, we define (f – g) : X \u2192 R by (f – g)(x) = f(x) – g(x) for all x \u2208 X<\/p>\n
Let f : X \u2192 R be a real-valued function and k be a scalar. Then, the product kf : X \u2192 R by (kf)(x) = kf (x) for all x \u2208 X<\/p>\n
Let f : X \u2192 R and g : X \u2192 R be any two real functions, where X \u2282 R . Then, we define fg : X \u2192 R by fg(x) = f(x) \u00d7 g(x) for all x \u2208 X<\/p>\n
Let f : X \u2192 R and g : X \u2192 R be any two real functions, where X \u2282 R. Then, we define \\(\\frac{f}{g}\\) : X \u2192 R by \n\\(\\left(\\frac{f}{g}\\right)(x)=\\frac{f(x)}{g(x)}\\) for all x \u2208 X<\/p>\n
We hope the Plus One Maths Notes Chapter 2 Relations and Functions help you. If you have any query regarding Kerala Plus One Maths Notes Chapter 2 Relations and Functions, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"
Plus One Maths Notes Chapter 2 Relations and Functions is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 2 Relations and Functions. Board SCERT, Kerala Text Book NCERT Based Class Plus One Subject Maths Notes Chapter Chapter 2 Chapter Name Relations and Functions Category Plus\u00a0One Kerala Kerala […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\n
Plus One Maths Notes Chapter 2 Relations and Functions - A Plus Topper<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n