Question

The range of the function $f\left(x\right)=x^2+2x+2$ is

• A. $\left(-1,\infty \right)$
• B. $\left(2,\infty \right)$
• C. $\left(0,\infty \right)$
• D. $\left(1,\infty \right)$
• E. $\left(-\infty ,\infty \right)$

Answer 1

Answer: (D)

Given, $f(x)=x^2+2x+2$
$=x^2+2x+1+1$
$=(x+1{)}^2+1\ge 1$
So, the range of $f(x)$ is $[1,\infty )$.