Consider the following three statements for the function f:(0,∞)→R defined by f(x)=∣logex∣−∣x−1∣ :
(I) f is differentiable at all x>0.
(II) f is increasing in (0,1).
(III) f is decreasing in (1,∞).
Then.
Held on 24 Jan 2026 · Verified 6 Jul 2026.
All (I), (II) and (III) are TRUE.
Only (II) and (III) are TRUE.
Only (I) is TRUE.
Only (I) and (III) are TRUE.
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