Question

below is the graph f(x)=(5x^3)-1, with a restricted domain. which best describes the domain of the inverse of the function?

Answer 1

The domain of the inverse of this function is the range of the function. So the domain of the inverse of this function is

-6 < x < 4.

Answer 2

The domain of the inverse function is -6 ≤ x ≤ 4.

Explanation:

The domain of a function is the set of all possible input values (x-values).

From inspection of the given graph, the endpoints are (-1, -6) and (1, 4).

The closed circles indicate the values are included in the interval.

Therefore, the domain of the graphed function is -1 ≤ x ≤ 1.

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph, the endpoint (-1, -6) is the minimum point and the endpoint (1, 4) is the maximum point.

The closed circles indicate the values are included in the interval.

Therefore, the range of the graphed function is -6 ≤ y ≤ 4.

The domain of the inverse function is the range of the original function (and the range of the inverse function is the domain of the original function).

Therefore, the domain of the inverse function is -6 ≤ x ≤ 4.

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Note: There is an error in the answer options. The domain includes both endpoints: -6 ≤ x ≤ 4.