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  4. If the domain of function g(x) is (0,1) then the domain of function y=g(2x)+g( ln |x|) is

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Q. 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

Relations and Functions - Part 2

Solution:

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, $x \in(-c,-1)$.