If h(x) = √(x - 4), which of the following is the domain of h(x)?

Rationale

√4 represents the correct domain of h(x) = √(x - 4).

The function h(x) = √(x - 4) is defined only when the expression inside the square root is non-negative. This condition requires that x - 4 ≥ 0, leading to the conclusion that x must be greater than or equal to 4, which includes the value √4 (the square root of 4).

A (√ 0) YOUR ANSWER

The expression √0 evaluates to 0, which is not the domain of the function h(x). The function h(x) is not defined for x values less than 4, and while 0 is a valid number, it does not satisfy the required condition for the function.

B (x > 0) YOUR ANSWER

While x > 0 includes all positive numbers, it does not specify the minimum value required for h(x) to be defined. Specifically, h(x) requires x to be at least 4, making this choice too broad and incorrect in the context of defining the domain.

C (√4) CORRECT

This choice accurately indicates that x must be at least 4 for h(x) to be defined, since √4 equals 2. The value 4 serves as the boundary for the domain, ensuring that the expression under the square root is non-negative, thus making this choice correct.

D (x > 4) YOUR ANSWER

Although x > 4 includes values greater than 4, it excludes the value 4 itself. The domain of h(x) must include 4, as it is the minimum value for which the function yields a real number output. Therefore, this choice does not encompass the entire domain.

Conclusion

The domain of the function h(x) = √(x - 4) is defined by the condition that x must be greater than or equal to 4. Among the given options, √4 correctly reflects this boundary value, while the other choices either misrepresent or fail to encapsulate the necessary domain. Understanding the domain is essential for determining the valid inputs for the function, ensuring its proper application in mathematical contexts.

If h(x) = √(x - 4), which of the following is the domain of h(x)?

√4 represents the correct domain of h(x) = √(x - 4).

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