Answer :
To determine the domain of the function
[tex]$$
h(x) = \sqrt{x-7} + 5,
$$[/tex]
we need to ensure that the expression inside the square root is non-negative, because the square root of a negative number is not defined in the set of real numbers. This requirement leads us to the inequality
[tex]$$
x - 7 \geq 0.
$$[/tex]
To solve this inequality, add 7 to both sides:
[tex]$$
x \geq 7.
$$[/tex]
Thus, the function is defined for all real numbers [tex]$x$[/tex] such that [tex]$x$[/tex] is greater than or equal to [tex]$7$[/tex]. This corresponds to option A, which states [tex]$x \geq 7$[/tex].
[tex]$$
h(x) = \sqrt{x-7} + 5,
$$[/tex]
we need to ensure that the expression inside the square root is non-negative, because the square root of a negative number is not defined in the set of real numbers. This requirement leads us to the inequality
[tex]$$
x - 7 \geq 0.
$$[/tex]
To solve this inequality, add 7 to both sides:
[tex]$$
x \geq 7.
$$[/tex]
Thus, the function is defined for all real numbers [tex]$x$[/tex] such that [tex]$x$[/tex] is greater than or equal to [tex]$7$[/tex]. This corresponds to option A, which states [tex]$x \geq 7$[/tex].
