Answer :
To determine the domain of the function \( f(x) = \sqrt{x-3} \), we need to consider the conditions under which the expression inside the square root is defined.
The square root function \( \sqrt{y} \) is only defined for \( y \geq 0 \). Therefore, for \( f(x) \) to be defined, the expression inside the square root \( x - 3 \) must be non-negative.
This leads to the inequality:
[tex]\[ x - 3 \geq 0 \][/tex]
This inequality can be solved by isolating \( x \). Adding 3 to both sides, we get:
[tex]\[ x \geq 3 \][/tex]
Thus, the inequality that ensures the function \( f(x) = \sqrt{x-3} \) is defined is:
[tex]\[ x - 3 \geq 0 \][/tex]
So, the correct inequality is:
[tex]\[ x - 3 \geq 0 \][/tex]
The square root function \( \sqrt{y} \) is only defined for \( y \geq 0 \). Therefore, for \( f(x) \) to be defined, the expression inside the square root \( x - 3 \) must be non-negative.
This leads to the inequality:
[tex]\[ x - 3 \geq 0 \][/tex]
This inequality can be solved by isolating \( x \). Adding 3 to both sides, we get:
[tex]\[ x \geq 3 \][/tex]
Thus, the inequality that ensures the function \( f(x) = \sqrt{x-3} \) is defined is:
[tex]\[ x - 3 \geq 0 \][/tex]
So, the correct inequality is:
[tex]\[ x - 3 \geq 0 \][/tex]
