Q. Let $f(x)=\log_ex$ and $g(x)=\frac{x^4-2x^3+3x^2-2x+2}{2x^2-2x+1}$. Then the domain of $f\circ g$ is
A) $[0,\infty)$
B) $[1,\infty)$
C) $(0,\infty)$
D) $\mathbb R$
Explanation
[Solution by Dr. Abubacker] $f\circ g$ needs $g(x)>0$. The denominator $2x^2-2x+1$ has discriminant $4-8<0$, so it is positive. The numerator is $(x^2-x+1)^2+1>0$. So $g(x)>0$ for all real $x$ and the domain is $\mathbb R$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.