Question 35

The domain of h(x) is x ≥ 4.

The function h(x) = √(x - 4) is defined when the expression under the square root is non-negative. Therefore, the domain of h(x) includes all values of x where x - 4 is greater than or equal to zero, which simplifies to x ≥ 4.

A) √ 0

This option does not represent a valid domain for the function. √0 equals 0, which does not provide any information about the values of x that can be input into h(x). The domain must be expressed in terms of x, not as a numerical value.

B) x > 0

While x > 0 includes many valid numbers, it does not encompass the correct domain for h(x). The function requires that x be at least 4 for the expression under the square root to be non-negative. Therefore, this option is incorrect.

C) √4

This option is misleading as it suggests a numeric value rather than a condition on x. However, √4 equals 2, which does not represent the actual domain of the function. The correct domain should express conditions on x, specifically x ≥ 4.

D) x > 4

This option is partially correct as it suggests that x must be greater than 4. However, the domain also includes the value x = 4, where h(x) is defined as h(4) = 0. Thus, the domain should be stated as x ≥ 4 rather than just x > 4.

Conclusion

The correct answer regarding the domain of h(x) is x ≥ 4, which encompasses all values for which the function is defined. Options A, B, and C fail to accurately describe the domain, while option D excludes the critical boundary value of x = 4. Hence, understanding the domain of functions involving square roots is essential for determining valid input values.