Final answer:
To determine f⁻¹(4) for f(x) = x³ - 3x, we solve x³ - 3x = 4 for x, which requires numerical methods or graphing to approximate the solution to be approximately 2.2136.
Step-by-step explanation:
To find the value of f⁻¹(4), where f⁻¹ represents the inverse function of f(x) = x³ - 3x, we need to solve the equation x³ - 3x = 4 for x. This equation cannot be factored easily, so we may have to use numerical methods or graphing to approximate the solution. However, if we plug in the numbers 1, 2, an so on, we can see that f(1) = -2, f(2) = 2, and f(3) = 18. The function is increasing, so there must be a solution between 2 and 3.
By using numerical methods like the bisection method or Newton-Raphson method, we can approximate the solution to be around 2.2136, which is the value of f⁻¹(4).