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If f: N to N, and x(2) gt x(1) implies f...

If `f: N to N, and x_(2) gt x_(1) implies f(x_(2)) gt f(x) AA x_(1), x_(2) in N and f(f(n))=3n AA n in N," then " f(2)=` _______.

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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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