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 obtained by swapping the elements of each ordered pair in the function. If \( f \) contains the pair \( (a, b) \), then the inverse function \( f^{-1} \) will contain the pair \( (b, a) \).

### Step 2: List the Ordered Pairs of the Function
The given function is:
\[ f = \{(2, 3), (3, 4), (4, 5)\} \]

### Step 3: Swap the Ordered Pairs
Now, we will swap the elements of each pair:
- From \( (2, 3) \), we get \( (3, 2) \)
- From \( (3, 4) \), we get \( (4, 3) \)
- From \( (4, 5) \), we get \( (5, 4) \)

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

### Final Answer
The inverse of the function \( f \) is:
\[ f^{-1} = \{(3, 2), (4, 3), (5, 4)\} \]

---