The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined. In the case of the function f(x) = 3√x, we need to determine the values of x that make the function meaningful.
To find the domain of f(x) = 3√x, we need to consider the restrictions on the square root function. The square root of a non-negative number is defined, but taking the square root of a negative number is not defined in the real number system. Therefore, the value inside the square root (√) must be greater than or equal to zero.
In this case, the expression inside the square root is x. So, we have the inequality x ≥ 0 to ensure that the square root is defined. This means that the function f(x) = 3√x is defined for all non-negative values of x.
Therefore, the domain of the function f(x) = 3√x is x ≥ 0, which can be expressed as [0, ∞). This means that any non-negative real number can be plugged into the function to obtain a valid output.
For example:
- If we substitute x = 4 into the function f(x) = 3√x, we get f(4) = 3√4 = 3 * 2 = 6.
- If we substitute x = 0 into the function f(x) = 3√x, we get f(0) = 3√0 = 3 * 0 = 0.
In summary, the domain of f(x) = 3√x is x ≥ 0, or [0, ∞), which means any non-negative real number can be used as input for the function.