Check Whether Given Function is One-One and Onto

📺 Video Explanation

📝 Question

Given:

\[ A=\{1,2,3\},\quad B=\{3,5,7\} \]

and function:

\[ f=\{(1,3),(2,5),(3,7)\} \]

Check whether the function is one-one and onto.

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✅ Solution

🔹 Check One-One (Injective)

A function is one-one if different inputs have different outputs.

Here:

• \(1 \mapsto 3\)
• \(2 \mapsto 5\)
• \(3 \mapsto 7\)

All outputs are distinct.

✔ Function is one-one.

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🔹 Check Onto (Surjective)

A function is onto if every element of codomain \(B\) has a pre-image.

Codomain:

\[ B=\{3,5,7\} \]

Range of function:

\[ \{3,5,7\} \]

Since range = codomain:

✔ Function is onto.

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🎯 Final Answer

\[ \boxed{\text{The function is both one-one and onto}} \]

So, it is a bijective function.

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🚀 Exam Shortcut

• Different outputs → one-one
• Range = codomain → onto
• Both true → bijection