Let . Then switch the positions of x and f(x) and change f(x) to y (since doing this switch changes f(x)).
Solve for y (i.e. ) in terms of x
Okay. You know that .find and verify the inverse function of f(x)=2x^3 - 4
The idea to find the inverse function of f, that is , is to get x in terms of y. Let , then we have . Add 4 in each sides of the equation, we get . Divide by 2 now, you get . Now take the 3rd root in each sides. You get finally that , or .
To verify it, just replace the x you had in your first equation by and if you find that it's equal to y, that means you did it.