Let f(x)= _ex and g(x)=x^4-2x^3+3x^2-2x+22x^2-2x+1.

Question

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

Accepted Answer

$\begin{gathered} f(x)=\ln x \ g(x)=\frac{{x}^{4}-2{x}^{3}+3{x}^{2}-2x+2}{2{x}^{2}-2x+1} \ {D}_{g}\in R \ {D}_{f}\in (0,\infty) \end{gathered}$

For ${D}_{fog}\Rightarrow g(x)>0$

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

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

Solutions · 1