Answer :
To find 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. This is because the square root of a negative number is not a real number.
Step 1: Set the expression inside the square root greater than or equal to zero.
[tex]$$
x - 7 \geq 0.
$$[/tex]
Step 2: Solve the inequality.
[tex]$$
x \geq 7.
$$[/tex]
This inequality tells us that the function is defined for all values of [tex]$x$[/tex] that are greater than or equal to [tex]$7$[/tex].
Thus, the correct answer is:
[tex]$$
x \geq 7.
$$[/tex]
Among the provided options, the domain [tex]$x \geq 7$[/tex] corresponds to option C.
[tex]$$
h(x)=\sqrt{x-7}+5,
$$[/tex]
we need to ensure that the expression inside the square root is non-negative. This is because the square root of a negative number is not a real number.
Step 1: Set the expression inside the square root greater than or equal to zero.
[tex]$$
x - 7 \geq 0.
$$[/tex]
Step 2: Solve the inequality.
[tex]$$
x \geq 7.
$$[/tex]
This inequality tells us that the function is defined for all values of [tex]$x$[/tex] that are greater than or equal to [tex]$7$[/tex].
Thus, the correct answer is:
[tex]$$
x \geq 7.
$$[/tex]
Among the provided options, the domain [tex]$x \geq 7$[/tex] corresponds to option C.
