Answer :
Sure! Let's find the domain of the function [tex]\( h(x) = \sqrt{x - 7} + 5 \)[/tex].
1. Understanding the Square Root:
The square root function is only defined for non-negative numbers. This means that whatever is inside the square root, in this case, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero.
2. Set the Expression ≥ 0:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the Inequality:
To solve this inequality, add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion about the Domain:
The domain of the function [tex]\( h(x) \)[/tex] is all the values of [tex]\( x \)[/tex] that satisfy the inequality [tex]\( x \geq 7 \)[/tex]. This means that the function can take any real number [tex]\( x \)[/tex] as an input, provided [tex]\( x \)[/tex] is greater than or equal to 7.
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
1. Understanding the Square Root:
The square root function is only defined for non-negative numbers. This means that whatever is inside the square root, in this case, [tex]\( x - 7 \)[/tex], must be greater than or equal to zero.
2. Set the Expression ≥ 0:
[tex]\[
x - 7 \geq 0
\][/tex]
3. Solve the Inequality:
To solve this inequality, add 7 to both sides:
[tex]\[
x \geq 7
\][/tex]
4. Conclusion about the Domain:
The domain of the function [tex]\( h(x) \)[/tex] is all the values of [tex]\( x \)[/tex] that satisfy the inequality [tex]\( x \geq 7 \)[/tex]. This means that the function can take any real number [tex]\( x \)[/tex] as an input, provided [tex]\( x \)[/tex] is greater than or equal to 7.
The correct answer is:
A. [tex]\( x \geq 7 \)[/tex]
