The range of the function $f (x) = (x^{2} + 2 x + 2)$ is

(1, \infty)

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(2, \infty)

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(0, \infty)

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[1, \infty)

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(- \infty, \infty)

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Solution

The correct option is C $[1, \infty)$
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 $[1, \infty)$ .

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