Let `f:R to R` be the function defined by `f(x)=2x-3, AA x in R.` Write `f^(-1).`

Explanation

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

### Step 1: Replace \( f(x) \) with \( y \)
Let \( y = f(x) \). Thus, we have:
\[ y = 2x - 3 \]

### Step 2: Solve for \( x \) in terms of \( y \)
We need to isolate \( x \). Start by adding 3 to both sides:
\[ y + 3 = 2x \]
Next, divide both sides by 2:
\[ x = \frac{y + 3}{2} \]

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

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

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