Let f

Question:

Let $\mathrm{f}, \mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}$ such that $\mathrm{f}(\mathrm{n}+1)=\mathrm{f}(\mathrm{n})+\mathrm{f}(a) \quad \forall \mathrm{n} \in \mathrm{N}$ and $\mathrm{g}$ be any arbitrary function. Which of the following statements is NOT true?

  1. (1) $\mathrm{f}$ is one-one

  2. (2) If fog is one-one, then $g$ is one-one

  3. (3) If $\mathrm{g}$ is onto, then fog is one-one

  4. (4) If $\mathrm{f}$ is onto, then $\mathrm{f}(\mathrm{n})=\mathbf{n} \forall \mathbf{n} \in \mathbf{N}$

Correct Option: , 2

Solution:

$f(n+1)=f(n)+1$

$f(2)=2 f(1)$

$f(3)=3 f(1)$

$f(4)=4 f(1)$

...

$f(n)=n f(1)$

$f(x)$ is one-one

 

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