{"id":"cb_question_bank:cfb12f26-38f2-4323-bca5-9246e30f5134","source_id":"cb_question_bank","source_item_id":"cfb12f26-38f2-4323-bca5-9246e30f5134","external_id":"e0bc2b05-f917-4d64-b9ad-36fa20c0b430","ibn":null,"question_id":"2cf7f039","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f left parenthesis x right parenthesis equals 8 StartRoot x EndRoot . For what value of x does f left parenthesis x right parenthesis equals 48 ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function <math alttext=\"f\"><mi>f</mi>\n</math> is defined by <math alttext=\"f left parenthesis x right parenthesis equals 8 StartRoot x EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>8</mn></mrow><msqrt><mi>x</mi></msqrt></math>. For what value of <math alttext=\"x\"><mi>x</mi>\n</math> does <math alttext=\"f left parenthesis x right parenthesis equals 48\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mrow><mn>48</mn></mrow></math>?</p>","rationale_html":"<p>Choice C is correct. It's given that <math alttext=\"f left parenthesis x right parenthesis equals 8 StartRoot x EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>8</mn><msqrt><mi>x</mi></msqrt></math>. Substituting <math alttext=\"48\"><mn>48</mn>\n</math> for&nbsp;<math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> in this equation yields <math alttext=\"48 equals 8 StartRoot x EndRoot\"><mn>48</mn><mo>=</mo><mn>8</mn><msqrt><mi>x</mi></msqrt></math>. Dividing both sides of this equation by <math alttext=\"8\"><mn>8</mn>\n</math> yields&nbsp;<math alttext=\"6 equals StartRoot x EndRoot\"><mn>6</mn><mo>=</mo><msqrt><mi>x</mi></msqrt></math>. This can be rewritten as <math alttext=\"StartRoot x EndRoot equals 6\"><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>6</mn></math>. Squaring both sides of this equation yields <math alttext=\"x equals 36\"><mi>x</mi><mo>=</mo><mn>36</mn></math>. Therefore, the value of <math alttext=\"x\"><mi>x</mi>\n</math> for which <math alttext=\"f left parenthesis x right parenthesis equals 48\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>48</mn></math> is <math alttext=\"36\"><mn>36</mn>\n</math>.</p>\n<p>Choice A is incorrect. If <math alttext=\"x equals 6\"><mi>x</mi><mo>=</mo><mn>6</mn></math>, <math alttext=\"f left parenthesis x right parenthesis equals 8 StartRoot 6 EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>8</mn><msqrt><mn>6</mn></msqrt></math>, not <math alttext=\"48\"><mn>48</mn>\n</math>.</p>\n<p>Choice B is incorrect. If <math alttext=\"x equals 8\"><mi>x</mi><mo>=</mo><mn>8</mn></math>, <math alttext=\"f left parenthesis x right parenthesis equals 8 StartRoot 8 EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>8</mn><msqrt><mn>8</mn></msqrt></math>, not <math alttext=\"48\"><mn>48</mn>\n</math>.</p>\n<p>Choice D is incorrect. If <math alttext=\"x equals 64\"><mi>x</mi><mo>=</mo><mn>64</mn></math>, <math alttext=\"f left parenthesis x right parenthesis equals 8 StartRoot 64 EndRoot\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>8</mn><msqrt><mn>64</mn></msqrt></math>, which is equivalent to <math alttext=\"64\"><mn>64</mn>\n</math>, not <math alttext=\"48\"><mn>48</mn>\n</math>.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.829000+00:00","source_updated_at":"2023-08-02T20:25:59.829000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"6\"><mn>6</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"8\"><mn>8</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"36\"><mn>36</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"64\"><mn>64</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}