Answer :
To find the domain of the function
$$
h(x)=\sqrt{x-7}+5,
$$
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 defined in the set of real numbers.
1. Set the expression inside the square root to be greater than or equal to zero:
$$
x - 7 \geq 0.
$$
2. Solve the inequality for $x$:
$$
x \geq 7.
$$
Thus, the domain of the function is all real numbers $x$ such that $x \geq 7$. Comparing with the given options, the correct answer is:
B. $\; x \geq 7$.
$$
h(x)=\sqrt{x-7}+5,
$$
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 defined in the set of real numbers.
1. Set the expression inside the square root to be greater than or equal to zero:
$$
x - 7 \geq 0.
$$
2. Solve the inequality for $x$:
$$
x \geq 7.
$$
Thus, the domain of the function is all real numbers $x$ such that $x \geq 7$. Comparing with the given options, the correct answer is:
B. $\; x \geq 7$.
