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:T47a,{"@context":"https://schema.org","@type":"Quiz","name":"Ap Eapcet 2024 Functions PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/ap-eapcet/questions/2024/mathematics/functions/m8vbeuw1","educationalLevel":"Entrance exam preparation","about":"Ap Eapcet / Mathematics / Functions","hasPart":{"@type":"Question","name":"Ap Eapcet 2024 Functions PYQ with Solution","text":"The range of the real valued function f(x)=\\left(\\frac{x^2+2 x-15}{2 x^2+13 x+15}\\right) is","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"To find the range of the function f(x) = \\frac{x^2 + 2x - 15}{2x^2 + 13x + 15} , we begin by factorizing the numerator and denominator. Denominator Factorization: 2x^2 + 13x + 15 = 0 2x^2 + 10x + 3x + 15 = 0 2x(x + 5) + 3(x + 5) = 0 (x + 5)(2x + 3) = 0 \\quad \\Rightarrow \\quad x = -5, \\frac{-3}{2} Numerator Factorization: x^2 + 2x - 15 = 0 x^2 + (5x - 3x) - 15 = 0 x(x + 5) - 3(x + 5) = 0 (x + 5)(x - 3) = 0 \\quad \\Rightarrow \\quad x = -5, 3 Domain and Range: The domain is (-\\infty, -5) \\cup (-5,..."}}}18:T422,

To find the range of the function $ f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} $, we begin by factorizing the numerator and denominator.

Denominator Factorization:

$ 2x^2 + 13x + 15 = 0 $

$ 2x^2 + 10x + 3x + 15 = 0 $

$ 2x(x + 5) + 3(x + 5) = 0 $

$ (x + 5)(2x + 3) = 0 \quad \Rightarrow \quad x = -5, \frac{-3}{2} $

Numerat

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