To find the domain of the function [tex]\( f(x) = \sqrt{22x - 44} \)[/tex], we need to determine for which values of [tex]\( x \)[/tex] the expression under the square root is non-negative. The square root function is only defined when the radicand (the expression inside the square root) is greater than or equal to zero.
Let's start with the inequality:
[tex]\[ 22x - 44 \geq 0 \][/tex]
1. Isolate [tex]\( x \)[/tex]:
Add 44 to both sides of the inequality:
[tex]\[ 22x \geq 44 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
Divide both sides by 22:
[tex]\[ x \geq 2 \][/tex]
Thus, the expression [tex]\( 22x - 44 \)[/tex] is non-negative when [tex]\( x \geq 2 \)[/tex]. Therefore, the function [tex]\( f(x) = \sqrt{22x - 44} \)[/tex] is defined for all [tex]\( x \)[/tex] where [tex]\( x \)[/tex] is greater than or equal to 2.
In interval notation, the domain of the function [tex]\( f(x) = \sqrt{22x - 44} \)[/tex] is:
[tex]\[ [2, \infty) \][/tex]
This interval includes all real numbers from 2 to infinity, where 2 is included in the domain.
