To determine the domain of the function [tex]\( f(x) = \sqrt{x + 26} \)[/tex], we need to ensure that the expression inside the square root is non-negative. This is because the square root function is only defined for non-negative values (i.e., [tex]\( \sqrt{y} \)[/tex] is defined only if [tex]\( y \geq 0 \)[/tex]).
We start with the inequality:
[tex]\[ x + 26 \geq 0 \][/tex]
To solve this inequality for [tex]\( x \)[/tex], we isolate [tex]\( x \)[/tex] by subtracting 26 from both sides:
[tex]\[ x \geq -26 \][/tex]
Therefore, the domain of the function [tex]\( f(x) = \sqrt{x + 26} \)[/tex] consists of all values [tex]\( x \)[/tex] such that [tex]\( x \geq -26 \)[/tex].
In conclusion, the domain is:
[tex]\[ x \geq -26 \][/tex]
