Question

find the inverse of f(x)=2x-7

Answer 1

To find the inverse of the function \( f(x) = 2x - 7 \), we follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 2x - 7
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 2y - 7
\]

3. **Solve for \( y \)**:
- Add 7 to both sides:
\[
x + 7 = 2y
\]
- Divide by 2:
\[
y = \frac{x + 7}{2}
\]

4. **Replace \( y \) with \( f^{-1}(x) \)**:
\[
f^{-1}(x) = \frac{x + 7}{2}
\]

So, the inverse of the function \( f(x) = 2x - 7 \) is:
\[
f^{-1}(x) = \frac{x + 7}{2}
\]