To find the domain of the function [tex]\( f(x) = \sqrt{x + 4} \)[/tex], we need to determine for which values of [tex]\( x \)[/tex] the function is defined.
1. The square root function, [tex]\( \sqrt{y} \)[/tex], is defined only for non-negative values of [tex]\( y \)[/tex]. Therefore, the expression inside the square root, [tex]\( x + 4 \)[/tex], must be greater than or equal to zero.
2. Set up the inequality:
[tex]\[
x + 4 \geq 0
\][/tex]
3. Solve the inequality for [tex]\( x \)[/tex]:
[tex]\[
x + 4 \geq 0 \implies x \geq -4
\][/tex]
4. The solution to the inequality tells us the set of [tex]\( x \)[/tex]-values for which the function is defined. These values form the domain of the function.
5. In interval notation, the domain is:
[tex]\[
[-4, \infty)
\][/tex]
So, the domain of [tex]\( f(x) = \sqrt{x + 4} \)[/tex] is [tex]\( x \)[/tex] such that [tex]\( x \geq -4 \)[/tex], which is written in interval notation as [tex]\( [-4, \infty) \)[/tex].
