JEE Main 2019 — Differentiation Question with Solution
From: JEE Main 2019 (Online) 10th April Evening Slot
Question
Let f(x) = loge(sin x), (0 < x < ) and g(x) = sin–1
(e–x
), (x 0). If is a positive real number such that
a = (fog)'() and b = (fog)(), then :
Choose an option
Show full solutionCorrect option: D
Correct answer
Da2 - b - a = 1
Step-by-step explanation
f(x) = ln(sin x), g(x) = sin–1 (e–x)
f(g(x)) = ln(sin(sin–1 e–x)) = -x
f(g()) = – = b
As f(g(x)) = – x
(f(g(x)))' = – 1
(f(g()))' = – 1 = a
b = – , a = – 1
a2 - b - a = - 2 + 2 + 1 = 1
f(g(x)) = ln(sin(sin–1 e–x)) = -x
f(g()) = – = b
As f(g(x)) = – x
(f(g(x)))' = – 1
(f(g()))' = – 1 = a
b = – , a = – 1
a2 - b - a = - 2 + 2 + 1 = 1
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This is a previous-year question from JEE Main 2019, covering the Differentiation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.