College

Select the correct answer.

What is the domain of the function [tex]h[/tex]?

[tex]h(x) = \sqrt{x - 7} + 5[/tex]

A. [tex]x \leq 5[/tex]

B. [tex]x \geq 7[/tex]

C. [tex]x \leq -7[/tex]

D. [tex]x \geq 5[/tex]

Answer :

To determine the domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex], we need to consider the expression inside the square root. The square root function is only defined for non-negative values, so that means [tex]\( x - 7 \)[/tex] must be greater than or equal to zero.

Step 1: Set up the inequality

For the square root to be defined, we have:

[tex]\[ x - 7 \geq 0 \][/tex]

Step 2: Solve the inequality

Add 7 to both sides of the inequality to find the values of [tex]\( x \)[/tex]:

[tex]\[ x \geq 7 \][/tex]

Conclusion:

The domain of the function [tex]\( h(x) = \sqrt{x-7} + 5 \)[/tex] is all values of [tex]\( x \)[/tex] such that [tex]\( x \geq 7 \)[/tex]. Therefore, the correct answer is:

B. [tex]\( x \geq 7 \)[/tex]