JEE Advanced | 2014FunctionHard
Question
Let f : (0, ∞) → R be given by f(x) = 
. Then
. ThenOptions
A.f(x) is monotonically increasing on [1, ∞)
B.f(x) is monotonically decreasing on (0, 1)
C.f(x) + f
= 0, for all x ∈ (0, ∞)
= 0, for all x ∈ (0, ∞)D.f(2x) is an odd function of x on R
Solution
f(x) = 
f′(x) =
> 0
Also, f(x) + f
and so, f(2x) + f(2-x) = 0
i.e., (A, C, D) is correct answer.
f′(x) =
> 0Also, f(x) + f
and so, f(2x) + f(2-x) = 0
i.e., (A, C, D) is correct answer.
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