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Let \( f, g: N \rightarrow N \) such that \( f(n+1)=f(n)+f(1)\) \(\forall n \in N \) and \( g \) be any arbitary functio…

Q1

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

[JEE Main 2021, 25 Feb (Shift 1)]

a

\( f \) is one-one

b

If \( f \circ g \) is one-one, then \( g \) is one-one

c

If \( g \) is onto, then \( f o g \) is one-one

d

If \( f \) is onto, then \( f(n)=n \forall n \in N \)

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