Answer :
To find the domain of the function
[tex]$$
h(x) = \sqrt{x - 7} + 5,
$$[/tex]
we must 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 in the set of real numbers.
1. Set the expression inside the square root to be greater than or equal to zero:
[tex]$$
x - 7 \geq 0.
$$[/tex]
2. Solve the inequality for [tex]$x$[/tex]:
[tex]$$
x \geq 7.
$$[/tex]
Therefore, the domain of the function is all real numbers [tex]$x$[/tex] such that [tex]$x \geq 7$[/tex].
The correct answer is:
B. [tex]$x \geq 7$[/tex].
[tex]$$
h(x) = \sqrt{x - 7} + 5,
$$[/tex]
we must 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 in the set of real numbers.
1. Set the expression inside the square root to be greater than or equal to zero:
[tex]$$
x - 7 \geq 0.
$$[/tex]
2. Solve the inequality for [tex]$x$[/tex]:
[tex]$$
x \geq 7.
$$[/tex]
Therefore, the domain of the function is all real numbers [tex]$x$[/tex] such that [tex]$x \geq 7$[/tex].
The correct answer is:
B. [tex]$x \geq 7$[/tex].
