For the function f, of, x, equals, 5, x, plus, 3f(x)=5x+3, find f, to the power minus 1 , left parenthesis, x, right parenthesisf

Question

−1
(x)

Answer 1

To find the inverse function \( f^{-1}(x) \) for the function \( f(x) = 5x + 3 \), we follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = 5x + 3 \]

2. Solve for \( x \): First, isolate \( x \) on one side of the equation: \[ y - 3 = 5x \] \[ x = \frac{y - 3}{5} \]

3. Swap \( x \) and \( y \) to express the inverse: \[ f^{-1}(x) = \frac{x - 3}{5} \]

The inverse function is: \[ f^{-1}(x) = \frac{x - 3}{5} \]

This is the final answer for \( f^{-1}(x) \).