Functions
Domain
MMTS_Full_Test_11
Grade 12
Question:
The domain of $f(x)$ is $(0,1)$, therefore, the domain of $y=f(e^x)+f(\ln|x|)$ is
$\left(\frac{1}{e},1\right)$
$(-e,-1)$
$\left(-1,-\frac{1}{e}\right)$
$(-e,-1)\cup(1,e)$
Step-by-Step Solution
Key Concept: Both $e^x\in(0,1)$ and $\ln|x|\in(0,1)$ simultaneously
$e^x\in(0,1)\Rightarrow x\in(-\infty,0)$. $\ln|x|\in(0,1)\Rightarrow|x|\in(1,e)\Rightarrow x\in(-e,-1)\cup(1,e)$. Intersection: $(-e,-1)$.
Correct Answer: 2