Mathematics · Functions

JEE Main 2025 — 23 January, Morning Shift — Question 6

Let $f(x)=\log _{e} x$ 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 fog is

Answer: A

$\mathrm{f}(\mathrm{x})=\ln \mathrm{x}$

$g(x)=\frac{x^{4}-2 x^{3}+3 x^{2}-2 x+2}{2 x^{2}-2 x+1}$

$D_{g} \in R$

$\mathrm{D}_{\mathrm{f}} \in(0, \infty)$

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

$\frac{x^{4}-2 x^{3}+3 x^{2}-2 x+2}{2 x^{2}-2 x+1}>0$

$\Rightarrow x^{4}-2 x^{3}+3 x^{2}-2 x+2>0$

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

Answer key and solution verified before publishing.

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