{"id":3537,"date":"2021-07-28T18:43:21","date_gmt":"2021-07-28T18:43:21","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3537"},"modified":"2021-11-24T16:13:29","modified_gmt":"2021-11-24T10:43:29","slug":"what-is-the-domain-and-range-of-modulus-function","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-domain-and-range-of-modulus-function\/","title":{"rendered":"What is the Domain and Range of Modulus Function"},"content":{"rendered":"

Here, you will learn modulus function and what is the domain and range of modulus function.<\/p>\n

Let’s begin –\"modulus<\/p>\n

The function f(x) defined by<\/p>\n

\n

y = |x| = \\(\\begin{cases} x & \\text{if}\\ x \\ge 0 \\\\ -x & \\text{if}\\ x < 0 \\end{cases}\\)<\/p>\n<\/blockquote>\n

is called the modulus function.<\/p>\n

It is also called absolute value function.<\/p>\n

we observe that the domain of the modulus function is the set R of all real numbers and the range is the set of all non-negative real numbers.\u00a0<\/p>\n

Domain and Range of Modulus Function<\/h2>\n

For f(x) = |x|,<\/p>\n

\n

Domain<\/strong> is R<\/p>\n

Range<\/strong> is [0,\\(\\infty\\)]<\/p>\n<\/blockquote>\n

The graph of the modulus function is as shown in figure, for x > 0, the graph coincides with the graph of the identity function i.e. the line y = x and for x > 0, it is coincident to the line y = -x,\u00a0<\/p>\n

The modulus function has the following properties :<\/p>\n

(i) For any real number x, we have<\/p>\n

\\(\\sqrt{x^2}\\) = |x|<\/p>\n

For example, \\(\\sqrt{cos^2x}\\)\u00a0 = | cos x |\u00a0 = \\(\\begin{cases} cos x ,\u00a0 & 0 \\ge x \\le \\pi\/2 \\\\ -cos x , & \\pi\/2 < x \\le \\pi \\end{cases}\\)<\/p>\n

(ii) If a, b are positive real numbers, then<\/p>\n

\\(x^2\\) \\(\\le\\) \\(a^2\\) \\(\\iff\\) |x| \\(\\le\\) a \\(\\iff\\) -a \\(\\le\\) x \\(\\le\\) a<\/p>\n

\\(x^2\\) \\(\\ge\\) \\(a^2\\) \\(\\iff\\) |x| \\(\\ge\\) a \\(\\iff\\) x \\(\\le\\) -a or, x \\(\\ge\\) a<\/p>\n

\\(x^2\\) < \\(a^2\\) \\(\\iff\\) |x| < a \\(\\iff\\) -a < x < a<\/p>\n

\\(x^2\\) > \\(a^2\\) \\(\\iff\\) |x| > a \\(\\iff\\)\u00a0 x < -a or, x > a<\/p>\n

\\(a^2\\) \\(\\le\\) \\(x^2\\) \\(\\le\\) \\(b^2\\) \\(\\iff\\) a \\(\\le\\) |x| \\(\\le\\) b \\(\\iff\\) x \\(\\in\\) [-b, -a] \\(\\cup\\) [a, b]<\/p>\n

\\(a^2\\) < \\(x^2\\) < \\(b^2\\) \\(\\iff\\) a < |x| < b \\(\\iff\\) x \\(\\in\\) (-b, -a) \\(\\cup\\) (a, b)<\/p>\n

(iii) For any real number x and y, we have<\/p>\n

| x + y | = | x | + | y |, if (x \\(\\ge\\) 0 and y \\(\\ge\\) 0) or, (x < 0 and y < 0)<\/p>\n

| x – y | = | x | – | y |, if (x \\(\\ge\\) 0 and | x | \\(\\ge\\) | y |) or, (x \\(\\ge\\) 0 and y \\(\\le\\) 0 and | x | \\(\\ge\\) | y |)<\/p>\n

| x \\(\\pm\\) y | \\(\\le\\) | x | + | y |<\/p>\n

| x \\(\\pm\\) y | > | | x | – | y | |<\/p>\n

Hope you learnt what is the domain and range of modulus function, learn more concepts of function\u00a0and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – One to One Function and Onto Function<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Domain and Range of Greatest Integer Function<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn modulus function and what is the domain and range of modulus function. Let’s begin – The function f(x) defined by y = |x| = \\(\\begin{cases} x & \\text{if}\\ x \\ge 0 \\\\ -x & \\text{if}\\ x < 0 \\end{cases}\\) is called the modulus function. It is also called absolute value function. …<\/p>\n

What is the Domain and Range of Modulus Function<\/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":[376,378,359,380,377,379],"yoast_head":"\nWhat is the Domain and Range of Modulus Function - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn modulus function and what is the domain and range of modulus 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\/what-is-the-domain-and-range-of-modulus-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Domain and Range of Modulus Function - 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