Ask a New Question
Menu

For the function f(x)=4x+2, find the f^-1(x)

1 answer

To find the inverse function \( f^{-1}(x) \) of the given function \( f(x) = 4x + 2 \), we will follow these steps:

  1. Replace \( f(x) \) with \( y \): \[ y = 4x + 2 \]

  2. Swap \( x \) and \( y \): \[ x = 4y + 2 \]

  3. Solve for \( y \): \[ x - 2 = 4y \] \[ y = \frac{x - 2}{4} \]

  4. Replace \( y \) with \( f^{-1}(x) \): \[ f^{-1}(x) = \frac{x - 2}{4} \]

Thus, the inverse function is: \[ f^{-1}(x) = \frac{x - 2}{4} \]