{"id":38384,"date":"2024-02-16T10:00:20","date_gmt":"2024-02-16T04:30:20","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=38384"},"modified":"2024-02-16T17:54:48","modified_gmt":"2024-02-16T12:24:48","slug":"plus-one-maths-notes-chapter-2","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-one-maths-notes-chapter-2\/","title":{"rendered":"Plus One Maths Notes Chapter 2 Relations and Functions"},"content":{"rendered":"

Plus One Maths Notes Chapter 2 Relations and Functions is part of Plus One Maths Notes<\/a>. Here we have given Kerala Plus One Maths Notes Chapter 2 Relations and Functions.<\/p>\n\n\n\n\n\n\n\n\n\n
Board<\/strong><\/td>\nSCERT, Kerala<\/td>\n<\/tr>\n
Text Book<\/strong><\/td>\nNCERT Based<\/td>\n<\/tr>\n
Class<\/strong><\/td>\nPlus One<\/td>\n<\/tr>\n
Subject<\/strong><\/td>\nMaths Notes<\/td>\n<\/tr>\n
Chapter<\/strong><\/td>\nChapter 2<\/td>\n<\/tr>\n
Chapter Name<\/strong><\/td>\nRelations and Functions<\/td>\n<\/tr>\n
Category<\/strong><\/td>\nPlus\u00a0One Kerala<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Kerala Plus One Maths Notes Chapter 2 Relations and Functions<\/h2>\n

I. Cartesian Product or Cross Product:<\/span>
\nThe Cartesian product between two sets A and B is denoted by A \u00d7 B is the set of all ordered pairs of elements from A and B.
\nie; A \u00d7 B = {(a, b): a \u2208 A, b \u2208 B}<\/p>\n

Properties:<\/p>\n

    \n
  1. In general A \u00d7 B \u2260 B \u00d7 A, but if A = B, A \u00d7 B = B \u00d7 A.<\/li>\n
  2. n(A \u00d7 B) = n(A) \u00d7 n(B)<\/li>\n
  3. n(A \u00d7 B) = n(B \u00d7 A)<\/li>\n<\/ol>\n

    II. Relations:<\/span>
    \nA relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product A \u00d7 B.<\/p>\n

    Representation of a relation:<\/p>\n

      \n
    1. Roster form<\/li>\n
    2. Set builder form<\/li>\n
    3. Arrow diagram.<\/li>\n<\/ol>\n

      Universal 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>\n

      If f : A \u2192 B is a function defined by f(x) = y.<\/p>\n

        \n
      1. The image of x = y<\/li>\n
      2. The pre-image of y = x<\/li>\n
      3. Domain of f = {x \u2208 A : f(x) \u2208 B}<\/li>\n
      4. Range of f = {f(x) : x \u2208 D(f)}<\/li>\n
      5. If f : A \u2192 B, then n(f) = n(B)n(A)<\/li>\n<\/ol>\n

        IV. Some Important Functions<\/span><\/p>\n

        Identity 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>\n

        Rational 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\"Plus
        \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\"Plus
        \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\"Plus
        \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>\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 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":"\nPlus One Maths Notes Chapter 2 Relations and Functions - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/plus-one-maths-notes-chapter-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus One Maths Notes Chapter 2 Relations and Functions\" \/>\n<meta property=\"og:description\" content=\"Plus One Maths Notes Chapter 2 Relations and Functions is part of Plus One Maths Notes. 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