If N be the set of all natural numbers, consider \( \Large f:N \rightarrow N:f \left(x\right)=2x \forall x \epsilon N \), then f is:
Correct Answer: Description for Correct answer:
Let \( \Large x_{1},x_{2} \epsilon N \), then \( f \left(x_{1}\right)=f \left(x_{2}\right) \)
=> \( \Large 2x_{1}=2x_{2} => x_{1}=x_{2} \)
Let y = 2x, then \( \Large x = \frac{y}{2} \notin N \)
Now, if we put y = 5, then \( \Large x = \frac{5}{2} \notin N \)
This shows that \( \Large 5 \epsilon N \), has no pre image in n
So, f is into
Hence, f is one-one into
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