16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T46b,{"@context":"https://schema.org","@type":"Quiz","name":"Ts Eamcet 2024 Functions PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/ts-eamcet/questions/2024/mathematics/functions/m64heu8e","educationalLevel":"Entrance exam preparation","about":"Ts Eamcet / Mathematics / Functions","hasPart":{"@type":"Question","name":"Ts Eamcet 2024 Functions PYQ with Solution","text":"The range of the real valued function f(x)=\\log _{3}\\left(5+4 x-x^{2}\\right) is","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"To determine the range of the function f(x) = \\log_3(5 + 4x - x^2) , we need to analyze the behavior of the quadratic expression 5 + 4x - x^2 . Analysis of 5 + 4x - x^2 The expression 5 + 4x - x^2 is a quadratic function of the form ax^2 + bx + c , where a = -1 , b = 4 , and c = 5 . Determining the Range of the Quadratic Since a = -1 Calculate the discriminant: D = 4^2 - 4 \\times (-1) \\times 5 = 16 + 20 = 36 The maximum value of the quadratic 5 + 4x - x^2 is: -\\frac{D}{4a} = -\\frac{36}{4 \\times..."}}}18:T5a5,

To determine the range of the function $ f(x) = \log_3(5 + 4x - x^2) $, we need to analyze the behavior of the quadratic expression $ 5 + 4x - x^2 $.

Analysis of $ 5 + 4x - x^2 $

The expression $ 5 + 4x - x^2 $ is a quadratic function of the form $ ax^2 + bx + c $, where $ a = -1 $, $ b = 4 $, and $ c = 5 $.

Determining the Range of the Quadratic

Since $ a = -1 < 0 $, the

Functions

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