Final answer:
To find an equation satisfying the domain requirements and data table, f(x) can be written as f(x) = k/x, where k is a constant. The function is neither even nor odd. The range of the function is (0, infinity).
Step-by-step explanation:
In this question, we are given the domain of the function f(x) as [0, [infinity]) and a data table representing the values of x and f(x).
To find an equation for f(x) that satisfies the domain requirements and the data table, we need to observe the pattern in the data table. We can see that as x increases, f(x) decreases.
Therefore, we can say that f(x) is inversely proportional to x. So, we can write the equation as f(x) = k/x, where k is a constant.
To find the value of k, we can use the first data point (x = 1, f(x) = 1/2). Substituting these values into the equation, we get 1/2 = k/1, which gives us k = 1/2.
Therefore, the equation for f(x) that satisfies the domain requirements and the data table is f(x) = (1/2) / x. We can verify this equation by substituting the given values of x into the equation and checking if we get the corresponding values of f(x) from the data table.
Now, let's determine if the function f(x) is even, odd, or neither. In this case, since the function is f(x) = (1/2) / x, we can see that f(-x) = (1/2) / -x = - (1/2) / x. So, f(-x) is not equal to f(x) and -f(x) = -((1/2) / x) = -f(x). Therefore, the function f(x) is neither even nor odd.
Finally, let's find the range of the function f(x). Since the domain of f(x) is [0, [infinity]), the minimum value that x can take is 0. As x approaches infinity, f(x) approaches 0. Therefore, the range of f(x) is (0, [infinity]).