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

$(- 1, e)$

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$(1, e)$

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$(- e, - 1)$

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$(- e, 1)$

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Solution

The correct option is C
$(- e, - 1)$

To find the domain of $f (e^{x}) + f (l n | x |)$ .
Given that the domain of f(x) is (0, 1)
$\Rightarrow 0 < e^{x} < 1 a n d 0 < l n | x | < 1 0 < e^{x} < 1 \Rightarrow x ϵ (- \infty, 0) . . . . . (i) 0 < l n | x | < 1 \Rightarrow 1 < | x | < e \Rightarrow x ϵ (- e, - 1) \cup (1, e) . . . . (i i)$

Combining (i) and (ii), the domain of $f (e^{x}) + f (l n | x |)$ is (-e,-1)

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