Question

Range of the function $f\left(x\right)=\frac{x^2+x+2}{x^2+x+1},x\in R$ is

• A. $(1,\infty )$
• B. $(1,\frac{11}{7})$
• C. $(1,\frac{7}{3})$
• D. $(1,\frac{7}{5})$

Answer 1

The correct option is A $(1,\infty )$

$f\left(x\right)=\frac{x^2+x+2}{x^2+x+1},x\in R$

Let $x^2+x=x$

Now, Range of $x^2+x$ will be

it is ef quadratic form, $(a>0)$

$[\frac{-D}{4a},\infty )\equiv [\frac{-1}{4},\infty )$

Now, Denominator of $f\left(x\right)$ con't be

zero.

$\begin{array}{cc}\text{Hence,}{R}_f& =(\frac{\infty +2}{\infty +1},\frac{-\frac{1}{4}+2}{\frac{-1}{4}+1})\\ & =(1,\frac{7}{3}]\end{array}$