{"id":18175,"date":"2026-05-02T22:28:52","date_gmt":"2026-05-02T16:28:52","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/domain-conditions-with-log-and-fraction-5\/"},"modified":"2026-05-02T22:28:52","modified_gmt":"2026-05-02T16:28:52","slug":"domain-conditions-with-log-and-fraction-5","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/domain-conditions-with-log-and-fraction-5\/","title":{"rendered":"Domain Conditions With Log And Fraction 5"},"content":{"rendered":"<p>For f(x)=log(x &#8211; 1) + 1\/(x + 8), which conditions must be satisfied? Select all correct options.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>x &gt; 1<\/li>\n<li>x &lt; 1<\/li>\n<li>x = -8<\/li>\n<li>x \u2265 1<\/li>\n<li>x = 1<\/li>\n<li>x \u2260 -8<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705,2717],"subject":[1425],"education_level":[1896],"class_list":["post-18175","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-functions","subject-mathematics","education_level-hsc"],"mcq_note":"For a domain question, check every part of the function separately. A logarithm is defined only when its input is positive, and a fraction is defined only when its denominator is not zero. Here, The logarithm requires x-1&gt;0, so x&gt;1. The denominator x+8 must not be zero, so x\u2260-8. Both restrictions are required. The final domain must satisfy both conditions at the same time, so both selected options are necessary.","mcq_options":[{"right":"yes","answer":"x &gt; 1"},{"right":"no","answer":"x &lt; 1"},{"right":"no","answer":"x = -8"},{"right":"no","answer":"x \u2265 1"},{"right":"no","answer":"x = 1"},{"right":"yes","answer":"x \u2260 -8"}],"multi_answers":"yes","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"},{"id":2717,"title":"Functions","slug":"functions"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/18175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=18175"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=18175"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=18175"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=18175"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=18175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}