Question

Function fx=1/2x³-3, find the inverse,

Answer 1

To find the inverse of the function f(x) = 1/2x³ - 3, you need to switch the roles of x and y and solve for y. The inverse function of f(x) = 1/2x³ - 3 is f^(-1)(x) = ∛(2x + 6).

Step-by-step explanation:

To find the inverse of the function f(x) = 1/2x³ - 3, we need to switch the roles of x and y and solve for y. Here are the steps:

1. Replace f(x) with y: y = 1/2x³ - 3
2. Swap x and y: x = 1/2y³ - 3
3. Solve for y by isolating it: 2x = y³ - 6
4. Rewrite the equation in the form y = (in order to get the cube root): y = ∛(2x + 6)

So, the inverse function of f(x) = 1/2x³ - 3 is f-1(x) = ∛(2x + 6).