Question

If the domain of function $g(x)$ is $(0,1)$ then the domain of function $y=g\left(2^x\right)+g(\ln |x|)$ is

• A. $(-1,0)$
• B. $(-1,-e/2)$
• C. $(-e,-1)$
• D. $(-c,1)$

Answer 1

Answer: (C)

Given, $D_g=(0,1)\Rightarrow 0<x<1$
$\therefore 0<2^x<1$ and $0<\ln |x|<1\Rightarrow -\infty <x<0$ and $1<|x|<$ e $\Rightarrow -\infty <x<0$ and $x\in (-e,-1)\cup (1,e)$
Hence, $x\in (-c,-1)$.