test","extracted_subject":"MATH","extracted_chapter":"FUCTIONS, LIMITS, CONTINIUITY AND DIFFTERENTIABILITY","extracted_topic":"FUNCTIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1594.png?top_left_x=0&top_left_y=0&width=532&height=469&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e6f425d76b7ab31beee","slug":"if-fgx-sinxand-gfx-sinsup2supsqrtxthen","content":"If f(g(x)) = \\|sinx\\|and g(f(x)) = sin²\$\\sqrt{x}\$then","options":[{"_id":"68a3b3837f15af4716bf8fbd","text":"f(x) = \$\\sqrt{x}\$, g(x) = sin²x","sequence":0,"isCorrect":true},{"_id":"68a3b3837f15af4716bf8fbe","text":"f(x) = sin\$\\sqrt{x}\$, g(x) = x²","sequence":1,"isCorrect":false},{"_id":"68a3b3837f15af4716bf8fbf","text":"f(x) = \$\\sqrt{\\sin x}\$, g(x) = x²","sequence":2,"isCorrect":false},{"_id":"68a3b3837f15af4716bf8fc0","text":"f(x) = \\|x\\|, g(x) = sin²x","sequence":3,"isCorrect":false}],"correct_answer":"f(x) = $\\sqrt{x}$, g(x) = sin²x","explanation":"Clearly f(x) =

, g(x) = sin²x satisfies both conditions.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:35.146Z","__v":0,"vector_store_id":"b9e8b071-1fc2-4015-b57c-e1f188bb8ce4","updated_at":"2024-08-30T21:49:35.146Z","isStarred":false},"params":{"questionSlug":"if-fgx-sinxand-gfx-sinsup2supsqrtxthen"}}]}]]

Question: If f(g(x)) = \|sinx\|and g(f(x)) = sin<sup>2</sup>\(\sqrt{x}\)then...

Solution