Cube Root Function
f(x) = ³√x
The cube root function, denoted by f(x) = ∛x, is a mathematical function that returns the cube root of a given input. It is the inverse of the cube function, f(x) = x³.
The domain of the cube root function is all real numbers, and the range is also all real numbers. However, when the input x is negative, the output is a complex number.
The graph of the cube root function is a curve that passes through the origin and has the shape of a half of a parabola that opens upward.
Some important properties of the cube root function include:
1. Because the cube root function is the inverse of the cube function, they are reflections of each other across the line y = x.
2. The cube root function is a one-to-one function, which means that each input has a unique output.
3. The cube root function is an odd function, which means that f(-x) = -f(x) for all values of x in the domain.
4. The cube root function is continuous and differentiable for all x in its domain.
5. The cube root function is used in various fields, including engineering, physics, and finance, where cube roots of values often arise.
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