# Q5 (2)  Find the range of each of the following functions         $f ( x ) = x ^2 +2$ , x is a real number.

Given function is

$f ( x ) = x ^2 +2$
It is given that  is a real  number
Now,
$\Rightarrow x^2 \geq 0$
Add 2 on both the sides
$\Rightarrow x^2+2 \geq 0+2$
$\Rightarrow f(x) \geq 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because f(x) = x^2+2)$
Therefore,
Range of function $f ( x ) = x ^2 +2$ is  $[2,\infty)$

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