67​–​78. Derivatives of inverse functions Consider the following functions (on the given interval, if specified). Find the derivative of the inverse function.


f(x) = 3x-4

Verified step by step guidance

1. Identify the function f(x) = 3x - 4 and recognize that we need to find its inverse function.
2. To find the inverse, set y = f(x), which gives y = 3x - 4, and then solve for x in terms of y.
3. Rearranging the equation, we get x = (y + 4) / 3, which means the inverse function is f^(-1)(y) = (y + 4) / 3.
4. Next, we will differentiate the inverse function f^(-1)(y) with respect to y using the derivative formula for inverse functions.
5. Apply the formula for the derivative of the inverse function, which states that if f'(x) is the derivative of f at x, then (f^(-1))'(y) = 1 / f'(x) evaluated at x = f^(-1)(y).