Most JEE Aspirants Got This WRONG | Inverse Function Trap
Автор: Factorial Academy
Загружено: 2026-02-27
Просмотров: 1533
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Most JEE Aspirants Got This WRONG | Inverse Function Trap | Factorial’s Question of the Day
Discussed this beautiful conceptual question in today’s episode of Factorial’s Question of the Day for JEE Advanced aspirants.
Given
f(x) = (−x³ + 15)/7
Let α be the number of real solutions of
f(x) = f⁻¹(x)
Let β be the number of real solutions of
f(x) = x
Find |α − β|.
Most students in the poll answered incorrectly.
The mistake? Blind algebra and no structural thinking.
In this session, we discussed:
• Why β = 1 (monotonic cubic insight)
• Why f(x) = f⁻¹(x) converts to f²(x) = x
• Proper factorisation of the 9th degree polynomial
• Mathematical proof that the quartic gives exactly 2 real roots
• Why total α = 5
• Final answer = 4
This is slightly lengthy for JEE Advanced, but the concepts tested are absolutely Advanced level:
Inverse functions, composition, monotonicity, derivative logic, root counting.
Join Telegram for daily advanced-level questions:
https://t.me/academyfactorial
Prepare smart. Think structurally.
— Factorial Academy
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#JEE2026
#JEEMaths2026
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#FunctionComposition
#JEEAdvancedMaths
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