{"id":9796,"date":"2022-01-27T16:38:44","date_gmt":"2022-01-27T11:08:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9796"},"modified":"2022-01-27T16:38:47","modified_gmt":"2022-01-27T11:08:47","slug":"what-is-homogeneous-function-definition-and-example","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-homogeneous-function-definition-and-example\/","title":{"rendered":"What is Homogeneous Function – Definition and Example"},"content":{"rendered":"

Here you will learn what is homogeneous function definition with example.<\/p>\n

Let’s begin –<\/p>\n

What is Homogeneous Function ?<\/h2>\n

Definition<\/strong> : A function is said to be homogeneous with respect to any set of variables when each of its terms is of the same degree with respect to those of the variables.<\/p><\/blockquote>\n

For example, \\(5x^2 + 3y^2 – xy\\) is homogeneous in x and y.<\/p>\n

Symbolically if, f(tx,ty) = \\(t^n\\)f(x, y) then f(x, y) is homogeneous function of degree n.<\/p>\n

Also Read<\/strong> : Types of Functions in Maths \u2013 Domain and Range<\/a><\/p>\n

Example<\/strong><\/span> : Which of the following function is not homogenous ?<\/p>\n

(i)  \\(x^3 + 8x^2y + 7y^3\\)<\/p>\n

(ii)  \\(y^2 + x^2 + 5xy\\)<\/p>\n

(iii)  \\(xy\\over x^2 + y^2\\)<\/p>\n

(iv)  \\(2x – y + 1\\over 2y – x + 1\\)<\/p>\n

Solution<\/strong><\/span> : \\(2x – y + 1\\over 2y – x + 1\\) is not homogenous because it does not have the same degree in each term.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is homogeneous function definition with example. Let’s begin – What is Homogeneous Function ? Definition : A function is said to be homogeneous with respect to any set of variables when each of its terms is of the same degree with respect to those of the variables. For example, \\(5x^2 …<\/p>\n

What is Homogeneous Function – Definition and Example<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[355,828,829],"yoast_head":"\nWhat is Homogeneous Function - Definition and Example<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is homogeneous function definition with examples based on it.\" \/>\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\/what-is-homogeneous-function-definition-and-example\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is Homogeneous Function - 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