Question

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

• A.
• B. ( 1 , 11/ 7]
• C. ( 1 , 7 / 3]
• D. ( 1, 7/5]

Answer 1

The correct option is C ( 1 , 7 / 3]

f(x) can also be written as:
$f\left(x\right)=1+\frac{1}{{(x+\frac{1}{2})}^2+\frac{3}{4}}\Rightarrow$ Range = (1,$\frac{7}{3}$).