f(x) = ∛x
The function f(x) = ∛x represents the cube root of x
The function f(x) = ∛x represents the cube root of x. In mathematical terms, given any input value x, the function calculates the number y such that y³ = x.
To better understand this function, let’s explain the concept of a cube root. If we have a number x, taking the cube root of x means finding a number y such that y³ = x. In other words, y is the number that, when multiplied by itself twice, gives x as the result.
For example, let’s consider the cube root of 27. We need to find a number y such that y³ = 27. By observing, we can see that 3 is the cube root of 27, since 3³ = 27. Similarly, the cube root of 8 is 2, since 2³ = 8.
Now, going back to the function f(x) = ∛x, when we input a number x, the function calculates its cube root and assigns that value to f(x). For instance, if we plug in x = 8, the function would return f(8) = ∛8 = 2.
It’s important to note that the cube root function has a domain of all real numbers and a range of all real numbers as well. This means it can be applied to any real number and will give us a real number as the result. Additionally, for negative values of x, the cube root will give us both positive and negative values as solutions.
For example, if we evaluate f(-27), f(-27) = ∛(-27) = -3, since (-3)³ = -27. This shows that -3 is also a valid solution for the cube root of -27.
To summarize, the function f(x) = ∛x represents the cube root of x and calculates the number y such that y³ = x for any real number x.
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