f(x) = x∧(1/3)
The function you provided is f(x) = x^(1/3)
The function you provided is f(x) = x^(1/3).
This function represents the cube root of x. To understand how to evaluate this function, we need to understand what it means to raise a number to the power of 1/3, which represents the cube root.
The cube root of a number is the value that, when multiplied by itself twice, gives the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27. Similarly, the cube root of -8 is -2, because -2 × -2 × -2 = -8.
To evaluate the function f(x) = x^(1/3), you need to substitute values of x and calculate the cube root of each of these values.
For example, let’s say we want to find the value of f(x) when x = 8. Plugging in x = 8 into the function, we get:
f(8) = 8^(1/3)
To calculate the cube root of 8, we need to find a number that, when multiplied by itself twice, gives 8. In this case, the cube root of 8 is 2, because 2 × 2 × 2 = 8.
Therefore, f(8) = 8^(1/3) = 2.
Similarly, if we want to find the value of f(x) when x = 64:
f(64) = 64^(1/3)
The cube root of 64 is 4, because 4 × 4 × 4 = 64.
Therefore, f(64) = 64^(1/3) = 4.
This process can be applied to any value of x. Just plug in the value of x and calculate the cube root to find the value of f(x).
I hope this explanation helps! If you have any further questions, feel free to ask.
More Answers:
The Intermediate Value Theorem: Proving the Existence of a Number c Such that f(c) = kUnderstanding the Difference Quotient and Limits for Calculating the Derivative
Exploring the Key Characteristics of the Cubic Function y=x³: Symmetry, Graph, Turning Points, and more.