Final answer:
The domain of the function h(x) is the set of all real numbers x such that x is less than or equal to 7/4, expressed in interval notation as (-∞, 7/4].
Step-by-step explanation:
To find the domain of the function h(x) = √(7-4x), we need to consider the values of x for which the expression under the square root is non-negative, since the square root of a negative number is not a real number. Therefore, we must find the values of x such that 7-4x ≥ 0. Solving this inequality gives us:
- 7 - 4x ≥ 0
- -4x ≥ -7
- x ≤ 7/4
The domain of h(x) is all real numbers x such that x ≤ 7/4. In interval notation, this is written as (-∞, 7/4].