"Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$. Then the domain of $f \circ g$ is"

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Accepted Answer

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$$\begin{aligned} & f(x)=\ln x \\ & g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1} \\ & D_g \in R \\ & D_f \in(0, \infty) \end{aligned}$$

For $D_{f o g} \Rightarrow g(x)>0$

$$\begin{aligned} & \frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}>0 \\ & \Rightarrow x^4-2 x^3+3 x^2-2 x+2>0 \end{aligned}$$

Clearly $\mathrm{x}<0$ satisfies which are included in option (1) only.

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Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$. Then the domain of $f \circ g$ is