Question

Find the inverse of the function f(x)=20x+3 Note: Enter your answer and SHOW ALL THE STEPS NECESSARY to solve this problem in the space provided. You will not receive credit without all work shown.

Answer 1

To find the inverse of the function \( f(x) = 20x + 3 \), we will follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 20x + 3
\]

2. **Swap \( x \) and \( y \)**:
To find the inverse, we need to exchange the roles of \( x \) and \( y \):
\[
x = 20y + 3
\]

3. **Solve for \( y \)**:
We will isolate \( y \) on one side of the equation. First, subtract 3 from both sides:
\[
x - 3 = 20y
\]
Now divide both sides by 20:
\[
y = \frac{x - 3}{20}
\]

4. **Write the inverse function**:
We now express the inverse function, which we denote as \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x - 3}{20}
\]

5. **Final Answer**:
Therefore, the inverse of the function \( f(x) = 20x + 3 \) is:
\[
f^{-1}(x) = \frac{x - 3}{20}
\]

This completes the process for finding the inverse of the given function.