JEE Main 2020 — Functions Question with Solution
From: JEE Main 2020 (Online) 6th September Evening Slot
Question
For a suitably chosen real constant a, let a
function, be defined by
. Further suppose that for any real number and ,
(fof)(x) = x. Then is equal to :
function, be defined by
. Further suppose that for any real number and ,
(fof)(x) = x. Then is equal to :
Choose an option
Show full solutionCorrect option: D
Correct answer
D3
Step-by-step explanation
Given,
and (fof)(x) = x
f(f(x)) = = x
= x
= x
(a2 – a) + x(a + 1) = (a2 + a)x + x2(a – 1)
a(a – 1) + x(1 – a2) – x2(a – 1) = 0
a = 1
f(x) =
So, = = 3
and (fof)(x) = x
f(f(x)) = = x
= x
= x
(a2 – a) + x(a + 1) = (a2 + a)x + x2(a – 1)
a(a – 1) + x(1 – a2) – x2(a – 1) = 0
a = 1
f(x) =
So, = = 3
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