Let f(x)= _e x and g(x)=(x^4-2 x^3+3 x^2-2 x+2)/(2 x^2-2 x+1).

Question

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

Accepted Answer

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

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

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

Solutions · 1