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If f: NvecN ,a n dx2> x1f(x2)>f(x1)AAx1,...

If `f: NvecN ,a n dx_2> x_1f(x_2)>f(x_1)AAx_1,x_2 in Na n df(f(n))=2nAAn in N ,` then `f(2)=_________`

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Verified by Experts

The correct Answer is:
3
`f(3n)=f(f(f(n))) = 3f(n) AA n in N`
Putting `n=1, f(3)=3f(1)`
If `f(f(1))=3 " giving " 1=3` which is absurd.
Therefore, `f(1) ne 1.`
Thus, `3=f(f(1)) gt f(1) gt 1`
So, `f(1)=2`
`f(2)=f(f(1)=3`
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