Consider the following three statements for the function defined by (I) is differentiable at all . (II) is increasing in (0, 1). (III) is decreasing in . Then. [2026]

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Solution

Q.
Consider the following three statements for the function $f : (0, \infty) \to ℝ$ defined by
$f (x) =$ $| \log_{e} x |$ $-$ $| x - 1 |$ $:$

(I) $f$ is differentiable at all $x > 0$ .

(II) $f$ is increasing in (0, 1).

(III) $f$ is decreasing in $(1, \infty)$ .

Then. [2026]

1 Only (I) and (III) are TRUE.

2 Only (II) and (III) are TRUE.

3 All (I), (II) and (III) are TRUE.

4 Only (I) is TRUE.

Ans.
(1)

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