Question

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

• A. $(0,\infty )$
• B. $(-\infty ,0)$
• C. $(0,5)$
• D. $(0,8)$

Answer 1

The correct option is A $(0,\infty )$

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

When,$x=0$

$f\left(0\right)=\frac{0+0+2}{0+0+1}$

When, $x<0$

$f\left(x\right)=\frac{x^2+x+2}{x^2+x+1}>0$

When, $x>0$

$f\left(x\right)=\frac{x^2+x+2}{x^2+x+1}>0$

So, the range of $f\left(x\right)$$=(0,\infty )$