First slide

Functions (XII)

Question

The domain of $f (x) is (0, 1)$ Then the domain of $f (e^{x}) + f (\ln |x|)$ is

Moderate

A

$(- 1, e)$
B

$(1, e)$
C

$(- e, - 1)$
D

$(- e, 1)$

Solution

$\begin{array}{l} f (x) is defined for x \in (0, 1) \\ So, f (e^{x}) + f (\ln |x|) is deffined for \\ 0 < e^{x} < 1 and 0 < \ln |x| < 1 \end{array}$
$\begin{array}{l} or - \infty < x < 0 and 1 < |x| < e \\ or x \in (- \infty, 0) and x \in (- e, - 1) \cup (1, e) \\ or x \in (- e, - 1) \end{array}$

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