Given the functions f(x) = 3x \u2212 1 and g(x) = 3x + 4, which operation results in the smallest coefficient on the x term?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine which operation results in the smallest coefficient on the ( x )-term between the functions ( f(x) = 3x – 1 ) and ( g(x) = 3x + 4 ), we need to evaluate the result of different operations, such as addition, subtraction, multiplication, and division. Here’s a breakdown of each operation:<\/p>\n\n\n\n [ [ [ [ The subtraction<\/strong> operation ( f(x) – g(x) ) results in the smallest coefficient on the ( x )-term, which is 0<\/strong>. This is because the ( x )-terms cancel each other out when the functions are subtracted. Therefore, the operation that gives the smallest coefficient on the ( x )-term is subtraction.<\/p>\n","protected":false},"excerpt":{"rendered":" Given the functions f(x) = 3x \u2212 1 and g(x) = 3x + 4, which operation results in the smallest coefficient on the x term? The Correct Answer and Explanation is: To determine which operation results in the smallest coefficient on the ( x )-term between the functions ( f(x) = 3x – 1 ) […]<\/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-168006","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168006","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=168006"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168006\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}1. Addition:<\/strong><\/h3>\n\n\n\n
(f + g)(x) = f(x) + g(x) = (3x – 1) + (3x + 4) = 3x + 3x – 1 + 4 = 6x + 3
]
The coefficient of ( x ) in the sum is 6<\/strong>.<\/p>\n\n\n\n2. Subtraction:<\/strong><\/h3>\n\n\n\n
(f – g)(x) = f(x) – g(x) = (3x – 1) – (3x + 4) = 3x – 1 – 3x – 4 = -5
]
The coefficient of ( x ) in the difference is 0<\/strong> (since the ( x )-terms cancel out).<\/p>\n\n\n\n3. Multiplication:<\/strong><\/h3>\n\n\n\n
(f \\cdot g)(x) = f(x) \\cdot g(x) = (3x – 1)(3x + 4)
]
Using the distributive property (FOIL method):
[
(3x)(3x) + (3x)(4) + (-1)(3x) + (-1)(4) = 9x^2 + 12x – 3x – 4 = 9x^2 + 9x – 4
]
The coefficient of ( x ) in the product is 9<\/strong>.<\/p>\n\n\n\n4. Division:<\/strong><\/h3>\n\n\n\n
\\frac{f(x)}{g(x)} = \\frac{3x – 1}{3x + 4}
]
To find the coefficient of ( x ), we can perform polynomial division. However, dividing the polynomials results in a more complex expression. The key takeaway here is that the linear term coefficient in the result is not simple to determine without more extensive algebraic manipulation. However, for simplicity in this context, we won’t delve deeper into this case.<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n