The Cubic Root Function: Definition And Properties

Cubic Root Function

A number that when multiplied three times equals the given number.

The cubic root function is a mathematical function that returns the cube root of a given input value. It is also known as the cube root function or the third root function. The symbol used to represent the cubic root function is ∛.

The cubic root function is defined as follows:

f(x) = ∛x

where x is the input value and f(x) is the output value, which is the cube root of x.

For example, if we want to find the cubic root of 8, we can use the cubic root function:

f(8) = ∛8 = 2

This means that the cube root of 8 is 2. Similarly, we can use the cubic root function to find the cube root of any other number.

One important property of the cubic root function is that it is an odd function. This means that if we apply the function to a negative number, we get a negative output. For example:

f(-8) = ∛(-8) = -2

This means that the cube root of -8 is -2.

The cubic root function can be graphed as a curve that starts in the negative numbers, passes through zero, and then continues into the positives. The slope of the curve is steepest at the origin and gradually becomes flatter as it moves away from the origin.

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