Question

Given the function f(x)=√−2x​, what is the domain of f?

A. All real values of x such that x=0.
B. All real values of x such that x≠0.
C. All real values of x such that x≤0.
D. All real values of x such that x≥0.
E. All real values of x.

Answer 1

The domain of the function f(x) = √(-2x) is all real values of x such that x ≤ 0, which allows the expression under the square root to be non-negative.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function f(x) = √(-2x), the expression under the square root must be non-negative, since the square root of a negative number is not defined within the realm of real numbers. Therefore, the value under the square root (-2x) must be greater than or equal to zero: -2x ≥ 0, which simplifies to x ≤ 0. Thus, the domain of f(x) is all real values of x such that x is less than or equal to zero, which corresponds to answer choice C: All real values of x such that x ≤ 0.