Final answer:
The expression -5√(x) makes sense for all non-negative real numbers; thus, the domain of the function is all real numbers x such that x ≥ 0.
Step-by-step explanation:
The student asks for what values of the variable the expression -5√(x) makes sense. In other words, the student wants to know the domain of this function. The square root of a number is defined for all non-negative real numbers, as negative numbers inside a square root result in non-real (imaginary) numbers, which are outside the scope of most high school mathematics curricula.
To determine the values for which -5√(x) is defined, we consider the expression inside the square root. The term x under the square root must be greater than or equal to zero (x ≥ 0). This is because the square root function produces real numbers only when the value under the root is non-negative. Hence, x can be equal to zero or any positive number, and the square root, multiplied by -5, will yield a real number. Therefore, the expression makes sense for all x ≥ 0.