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The function f:NtoN,N being the set of o...

The function `f:NtoN,N` being the set of of natural numbers, defined by f(x)=2x+3 is

A

injective and surjective

B

injective but not surjective

C

not injective but surjective

D

neither injective nor surjective

Text Solution

Verified by Experts

The correct Answer is:
B
Given `f:NtoN`
`:.f(x)=2x+3impliesf'(x)=2gt0`
So, f(x) is increasing, `AAx""inN`.
Hence, f(x) is injective.
Let f(x)=y
`impliesy=2x+3impliesx=(y-3)/(2)`
This is injective
`:.x=(1)/(2)`
and `yinN" but "x""inN`
Hence,k f(x) is not surjective.
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