Find \(f^{-1}\)
📝 Question
Let:
\[ A=\{a,b,c,d\} \]
\[ f=\{(a,b),(b,d),(c,a),(d,c)\} \]
Find \(f^{-1}\).
✅ Solution
🔹 Step 1: Definition of inverse
The inverse of a function is obtained by reversing each ordered pair:
\[ (x,y) \Rightarrow (y,x) \] —
🔹 Step 2: Reverse each pair
\[ (a,b) \Rightarrow (b,a) \]
\[ (b,d) \Rightarrow (d,b) \]
\[ (c,a) \Rightarrow (a,c) \]
\[ (d,c) \Rightarrow (c,d) \] —
🔹 Step 3: Write inverse function
\[ f^{-1}=\{(b,a),(d,b),(a,c),(c,d)\} \] —
🎯 Final Answer
\[ \boxed{f^{-1}=\{(b,a),(d,b),(a,c),(c,d)\}} \]
🚀 Exam Shortcut
- Just reverse ordered pairs
- No calculation needed
- Works only if function is one-one