If `f(x)=2x-3`, the inverse of `f,f^(-1)` could be represented by

Options

A. `f^(-1)(x)=3x-2`
B. `f^(-1)(x)=(1)/(2x-3)`
C. `f^(-1)(x)=(x-2)/(3)`
D. `f^(-1)(x)=(x+3)/(2)`

Explanation

To find the inverse of the function \( f(x) = 2x - 3 \), we will follow these steps:

### Step-by-Step Solution:

1. **Replace \( f(x) \) with \( y \)**:
\[ y = 2x - 3 \]

2. **Isolate \( x \)**:
- First, add 3 to both sides:
\[ y + 3 = 2x \]
- Next, divide both sides by 2:
\[ x = \frac{y + 3}{2} \]

3. **Express the inverse function**:
- We can now express the inverse function \( f^{-1}(x) \) by replacing \( y \) with \( x \):
\[ f^{-1}(x) = \frac{x + 3}{2} \]

### Final Answer:
Thus, the inverse of the function \( f(x) = 2x - 3 \) is:
\[ f^{-1}(x) = \frac{x + 3}{2} \]