If `f = {(2,3) ,(3,4) , (4,5}`, then its inverse is :

Options

A. `{(3,4) , (4,5) , (3,2)}`
B. `{(3,2) , (4,3) , (5,4)}`
C. `{(2,3) , (4, 3) , (5,4)}`
D. None of these

Answer

To find the inverse of the function \( f = \{(2,3), (3,4), (4,5)\} \), we will follow these steps:

### Step 1: Understand the Definition of Inverse Function
The inverse of a function \( f \) is a function \( f^{-1} \) that reverses the mapping of \( f \). If \( f(a) = b \), then \( f^{-1}(b) = a \).

### Step 2: Identify the Ordered Pairs
The given function \( f \) consists of the ordered pairs:
- \( (2, 3) \)
- \( (3, 4) \)
- \( (4, 5) \)

### Step 3: Reverse the Ordered Pairs
To find the inverse function, we will reverse each ordered pair:
- The pair \( (2, 3) \) becomes \( (3, 2) \)
- The pair \( (3, 4) \) becomes \( (4, 3) \)
- The pair \( (4, 5) \) becomes \( (5, 4) \)

### Step 4: Write the Inverse Function
The inverse function \( f^{-1} \) is thus:
\[ f^{-1} = \{(3, 2), (4, 3), (5, 4)\} \]

### Step 5: Conclusion
The inverse of the function \( f \) is \( f^{-1} = \{(3, 2), (4, 3), (5, 4)\} \).

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