Inverse of the function `y =2x -3` is

Options

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

Answer

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

### Step 1: Write the function in terms of \( y \)
The given function is:
\[ y = 2x - 3 \]

### Step 2: Swap \( x \) and \( y \)
To find the inverse, we swap \( x \) and \( y \):
\[ x = 2y - 3 \]

### Step 3: Solve for \( y \)
Now, we need to solve this equation for \( y \):
1. Add 3 to both sides:
\[ x + 3 = 2y \]
2. Divide both sides by 2:
\[ y = \frac{x + 3}{2} \]

### Step 4: Write the inverse function
Now that we have \( y \) in terms of \( x \), we can write the inverse function:
\[ f^{-1}(x) = \frac{x + 3}{2} \]

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

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