Question

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
−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 \( f^{-1}(x) \).