Question

What is the domain of the function f(x) = 4x⁵?

1) 0 < x < 50
2) x > 0
3) x < 50
4) x > 0 and x < 50

Answer 1

The domain of the function f(x) = 4x^5 is all real numbers, as polynomial functions are defined for every real number. None of the provided options correctly represent the domain which should be (-∞, ∞).

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. Looking at the function f(x) = 4x5, this is a polynomial function, which is defined for all real numbers. There are no restrictions on x since polynomial functions are continuous and well-defined for all real values. Thus, the domain of f(x) = 4x5 is all real numbers, or in interval notation, (-∞, ∞). None of the provided options correctly represent the domain of this function. Options 1, 2, 3, and 4 all suggest some restrictions on the domain, but since there are none for a polynomial function, all are incorrect in this context.