Let f(x) = loge x and g(x) = x^4-2x^3+3x^2-2x+2/2x62-2x+1. Then the domain of fog is

Question

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

(1) \(\mathbb{R}\)

(2) \((0, \infty)\)

(3) \([0, \infty)\)

(4) \([1, \infty)\)

Answer 1

Correct option is (1) \(\mathbb{R}\)  

\(\mathrm{f}(\mathrm{x})=In\ \mathrm{x}\)

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

\(D_{g} \in R\)

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

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.