{"id":259502,"date":"2025-07-19T02:43:09","date_gmt":"2025-07-19T02:43:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259502"},"modified":"2025-07-19T02:43:11","modified_gmt":"2025-07-19T02:43:11","slug":"find-the-domain-of-the-following-piecewise-function-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/find-the-domain-of-the-following-piecewise-function-2\/","title":{"rendered":"find the domain of the following piecewise function"},"content":{"rendered":"\n

find the domain of the following piecewise function. f(x) 3x-2 if -1 2x+3 if 0<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s first define the piecewise function and understand how to find its domain.<\/p>\n\n\n\n

The function is given as: f(x)={3x\u22122if x\u2264\u221212x+3if x>0f(x) = \\begin{cases} 3x – 2 & \\text{if } x \\leq -1 \\\\ 2x + 3 & \\text{if } x > 0 \\end{cases}f(x)={3x\u221222x+3\u200bif x\u2264\u22121if x>0\u200b<\/p>\n\n\n\n

Finding the Domain:<\/h3>\n\n\n\n

The domain of a function is the set of all possible values of xxx for which the function is defined.<\/p>\n\n\n\n

In this case, we have two pieces to consider:<\/p>\n\n\n\n

    \n
  1. The first piece, 3x\u221223x – 23x\u22122, is defined for x\u2264\u22121x \\leq -1x\u2264\u22121. This means that this part of the function is valid for values of xxx less than or equal to \u22121-1\u22121.<\/li>\n\n\n\n
  2. The second piece, 2x+32x + 32x+3, is defined for x>0x > 0x>0. This means that this part of the function is valid for values of xxx strictly greater than 0.<\/li>\n<\/ol>\n\n\n\n

    Domain of the Piecewise Function:<\/h3>\n\n\n\n
      \n
    • The first part is valid for x\u2264\u22121x \\leq -1x\u2264\u22121, so we include all values less than or equal to \u22121-1\u22121.<\/li>\n\n\n\n
    • The second part is valid for x>0x > 0x>0, so we include all values greater than 0.<\/li>\n<\/ul>\n\n\n\n

      The important thing to notice here is that there is no piece of the function defined for \u22121<x\u22640-1 < x \\leq 0\u22121<x\u22640. Therefore, there is a gap between the two pieces of the function, meaning no value of xxx exists between \u22121-1\u22121 and 0 in this case.<\/p>\n\n\n\n

      Conclusion:<\/h3>\n\n\n\n

      The domain of the piecewise function is: (\u2212\u221e,\u22121]\u222a(0,\u221e)(-\\infty, -1] \\cup (0, \\infty)(\u2212\u221e,\u22121]\u222a(0,\u221e)<\/p>\n\n\n\n

      This means the function is defined for all xxx values that are either less than or equal to \u22121-1\u22121, or greater than 0. However, it is not defined for values in the interval (\u22121,0](-1, 0](\u22121,0].<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      find the domain of the following piecewise function. f(x) 3x-2 if -1 2x+3 if 0 The Correct Answer and Explanation is: Let’s first define the piecewise function and understand how to find its domain. The function is given as: f(x)={3x\u22122if x\u2264\u221212x+3if x>0f(x) = \\begin{cases} 3x – 2 & \\text{if } x \\leq -1 \\\\ 2x + 3 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-259502","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259502","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=259502"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259502\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}