What is range of $x^{2} + 5$

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Solution

Assuming that the domain of the given function is R meaning that x takes all values in the interval $(- \infty, + \infty)$ which means that $x^{2}$ is either zero or positive. Hence we can write the following inequality
$x^{2} \leq 0$
Add 5 to both sides of the inequality to obtain the inequality
$x^{2} + 5 \leq= 0 + 5 o r f (x) \leq 5$
The range of $f (x) = x^{2} + 5$ is given by the interval: $[5, + \infty)$

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