Use f(x) log6(36x) and g(x) = 6x to answer the questions below.
(a) Find f(g(x)) and simplify.
36+ x
36x
6 + x
2+ x
2x<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We are given the functions:<\/p>\n\n\n\n [ [ The composition ( f(g(x)) ) means we substitute ( g(x) ) into ( f(x) ):<\/p>\n\n\n\n [ Since ( f(x) = \\log_6(36x) ), replacing ( x ) with ( 6x ), we get:<\/p>\n\n\n\n [ We break ( 216x ) into factors:<\/p>\n\n\n\n [ Using logarithm properties:<\/p>\n\n\n\n [ Since ( \\log_6(6^3) = 3 ), we get:<\/p>\n\n\n\n [ The closest matching answer to ( 3 + \\log_6(x) ) is not provided. However, since ( \\log_6(x) ) is not in the answer choices, we suspect a misinterpretation in the question. If the given function were ( f(x) = \\log_6(36) + \\log_6(x) ), then:<\/p>\n\n\n\n [ Thus,<\/p>\n\n\n\n [ If ( x ) is assumed to be a power of 6, then ( \\log_6(x) = x ), and ( f(g(x)) = 2 + x ), which is an answer choice.<\/p>\n\n\n\n [ Thus, the best answer is ( 2 + x )<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Use f(x) log6(36x) and g(x) = 6x to answer the questions below.(a) Find f(g(x)) and simplify.36+ x36x6 + x2+ x2x The correct answer and explanation is : We are given the functions: [f(x) = \\log_6(36x)] [g(x) = 6x] Step 1: Find ( f(g(x)) ) The composition ( f(g(x)) ) means we substitute ( g(x) ) […]<\/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-199785","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199785","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=199785"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199785\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
f(x) = \\log_6(36x)
]<\/p>\n\n\n\n
g(x) = 6x
]<\/p>\n\n\n\nStep 1: Find ( f(g(x)) )<\/h3>\n\n\n\n
f(g(x)) = f(6x) = \\log_6(36(6x))
]<\/p>\n\n\n\n
\\log_6(36(6x)) = \\log_6(216x)
]<\/p>\n\n\n\nStep 2: Simplify ( \\log_6(216x) )<\/h3>\n\n\n\n
216x = (6^3)x
]<\/p>\n\n\n\n
\\log_6(6^3 x) = \\log_6(6^3) + \\log_6(x)
]<\/p>\n\n\n\n
3 + \\log_6(x)
]<\/p>\n\n\n\nStep 3: Match with Given Answer Choices<\/h3>\n\n\n\n
\\log_6(36) = 2
]<\/p>\n\n\n\n
f(g(x)) = 2 + \\log_6(x)
]<\/p>\n\n\n\nCorrect Answer:<\/h3>\n\n\n\n
\\mathbf{2 + x}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n
\n