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