Check Whether the Function is One-One
📝 Question
Let:
\[ A=\{1,2,3\}, \quad B=\{4,5,6,7\} \]
\[ f=\{(1,4),(2,5),(3,6)\} \]
Check whether \(f\) is one-one.
✅ Solution
🔹 Step 1: Definition of one-one
A function is one-one if different elements of domain have different images.
—🔹 Step 2: Check images
\[ f(1)=4,\quad f(2)=5,\quad f(3)=6 \]
All outputs are different.
—🔹 Step 3: Conclusion
No two elements of \(A\) have the same image.
Hence, \(f\) is one-one (injective).
—🎯 Final Answer
\[ \boxed{\text{f is one-one}} \]
🚀 Exam Shortcut
- Check outputs (second elements)
- If all are distinct ⇒ one-one
- If any repeat ⇒ not one-one