Which of the following is the domain of the absolute value function f(x) = |x – 4x^2|? Option 1: All real numbers Option 2: x ≤ 0 Option 3: x ≥ 0 Option 4: -[infinity] < x &l…

Question

Which of the following is the domain of the absolute value function f(x) = |x – 4x^2|? Option 1: All real numbers Option 2: x ≤ 0 Option 3: x ≥ 0 Option 4: -[infinity] < x < [infinity]

Answer 1

The domain of the function f(x) = |x – 4x^2| is all real numbers, which can be represented as -[infinity] < x < [infinity].

Step-by-step explanation:

The domain of a function is the all set of x-values for which the function is defined. Basically, it's the set of all possible input values. In the case of the absolute value function f(x) = |x – 4x^2|, this function is well-defined for all real numbers. This is because you can insert any real value of x, whether a positive number, a negative number, or zero, into the function f(x), and it will yield a real number output. Thus, of the list of options provided, Option 4: -[infinity] < x < [infinity], also referred to as all real numbers, is the domain for this absolute value function.

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