{"id":4055,"date":"2021-08-15T15:03:10","date_gmt":"2021-08-15T15:03:10","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4055"},"modified":"2022-01-27T16:36:46","modified_gmt":"2022-01-27T11:06:46","slug":"algebraic-operations-on-functions","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/algebraic-operations-on-functions\/","title":{"rendered":"Algebraic Operations on Functions"},"content":{"rendered":"

Here you will learn algebraic operations on functions, equal or identical functions and homogeneous function.<\/p>\n

Let’s begin –<\/p>\n

Algebraic Operations on Functions<\/h2>\n

Various operations, namely addition, subtraction, multiplication, division etc on real function are :<\/p>\n

(i) Addition<\/strong> : Let f : \\(D_1\\) \\(\\rightarrow\\) R and g : \\(D_2\\) \\(\\rightarrow\\) R be two real functions. Then, their sum f + g is defined from \\(D_1 \\cap D_2\\) to R which associates each x \\(\\in\\) \\(D_1 \\cap D_2\\) to the number f(x) + g(x). It is defined as<\/p>\n

(f + g) (x) = f(x) + g(x)\u00a0 for all\u00a0 x \\(\\in\\) \\(D_1 \\cap D_2\\)<\/p>\n

(ii) Difference (Subtraction)<\/strong> : Let f : \\(D_1\\) \\(\\rightarrow\\) R and g : \\(D_2\\) \\(\\rightarrow\\) R be two real functions. Then, the difference of g from f is denoted by f – g and is defined as<\/p>\n

(f – g) (x) = f(x) – g(x)\u00a0 for all\u00a0 x \\(\\in\\) \\(D_1 \\cap D_2\\)<\/p>\n

(iii) Product<\/strong> : Let f : \\(D_1\\) \\(\\rightarrow\\) R and g : \\(D_2\\) \\(\\rightarrow\\) R be two real functions. Then, their product (or pointwise multiplication) f g is a function \\(D_1 \\cap D_2\\) to R and is defined as<\/p>\n

(f g) (x) = f(x) g(x)\u00a0 for all\u00a0 x \\(\\in\\) \\(D_1 \\cap D_2\\)<\/p>\n

(iv) Quotient<\/strong> : Let f : \\(D_1\\) \\(\\rightarrow\\) R and g : \\(D_2\\) \\(\\rightarrow\\) R be two real functions. Then, the quotient of f by g is denoted by \\(f\\over g\\) and it is a function from \\(D_1 \\cap D_2\\) – {x : g(x) = 0} to R defined by<\/p>\n

(\\(f\\over x\\))(x) = \\(f(x)\\over g(x)\\) for all\u00a0 x \\(\\in\\) \\(D_1 \\cap D_2\\) – {x : g(x) = 0}<\/p>\n

(v) Multiplication of a function by a scalar<\/strong> : Let f : D \\(\\rightarrow\\) R be a real function and \\(\\alpha\\) be a scalar (real number). Then the product \\(\\alpha\\)f is a function from D to R and is defined as<\/p>\n

\\(\\alpha f\\) (x) = \\(\\alpha\\) f(x) for all x \\(\\in\\) D<\/p>\n\n\n

Example : <\/span> Find the domain of the function y = \\(log_{(x-4)}(x^2 – 11x + 24)\\).<\/p>\n

Solution : <\/span>Here ‘y’ would assume real value if,

\n x – 4 > 0 and \\(\\ne\\) 1, \\(x^2 -11x + 24\\) > 0 \\(\\implies\\) x > 4 and \\(\\ne\\) 5, (x-3)(x-8) > 0

\n \\(\\implies\\) x > 4 and \\(\\ne\\) 5, x < 3 or x > 8 \\(\\implies\\) x > 8 \\(\\implies\\) Domain (y) = (8, \\(\\infty\\))

<\/p>\n\n\n

Bounded Function<\/strong><\/h4>\n

A function is said to be bounded if there exists a finite M such that |f(x)| \\(\\le\\) M, \\(\\forall\\) x \\(\\in\\) \\(D_f\\).<\/p>\n\n\n

<\/div>\n\n\n\n
\n
Previous – What is Inverse of a Function<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn algebraic operations on functions, equal or identical functions and homogeneous function. Let’s begin – Algebraic Operations on Functions Various operations, namely addition, subtraction, multiplication, division etc on real function are : (i) Addition : Let f : \\(D_1\\) \\(\\rightarrow\\) R and g : \\(D_2\\) \\(\\rightarrow\\) R be two real functions. Then, …<\/p>\n

Algebraic Operations on Functions<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[353,356],"yoast_head":"\nAlgebraic Operations on Functions - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn algebraic operations on functions, equal or identical functions and homogeneous function.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/algebraic-operations-on-functions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algebraic Operations on Functions - 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