Answer :
To find the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex], we need to determine for which values of [tex]\( x \)[/tex] the function is defined.
1. Understand the condition for the square root: The expression inside the square root, [tex]\( x - 7 \)[/tex], must be non-negative, because the square root of a negative number is not a real number. This means:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality: To find the values of [tex]\( x \)[/tex] that satisfy this inequality, we solve it by adding 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
3. Determine the domain: So, the domain of [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7.
Given the options, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
1. Understand the condition for the square root: The expression inside the square root, [tex]\( x - 7 \)[/tex], must be non-negative, because the square root of a negative number is not a real number. This means:
[tex]\[
x - 7 \geq 0
\][/tex]
2. Solve the inequality: To find the values of [tex]\( x \)[/tex] that satisfy this inequality, we solve it by adding 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
3. Determine the domain: So, the domain of [tex]\( h(x) \)[/tex] is all values of [tex]\( x \)[/tex] that are greater than or equal to 7.
Given the options, the correct answer is:
B. [tex]\( x \geq 7 \)[/tex]
