jee-main 2021 Q72

jee-main · India · session1_25feb_shift1 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let $f , g : N \rightarrow N$ such that $f ( n + 1 ) = f ( n ) + f ( 1 ) \forall n \in N$ and $g$ be any arbitrary function. Which of the following statements is NOT true?
(1) If $f$ is onto, then $f ( n ) = n \forall n \in N$
(2) If $g$ is onto, then $f o g$ is one-one
(3) $f$ is one-one
(4) If $f \circ g$ is one-one, then $g$ is one-one

Let $f , g : N \rightarrow N$ such that $f ( n + 1 ) = f ( n ) + f ( 1 ) \forall n \in N$ and $g$ be any arbitrary function. Which of the following statements is NOT true?\\
(1) If $f$ is onto, then $f ( n ) = n \forall n \in N$\\
(2) If $g$ is onto, then $f o g$ is one-one\\
(3) $f$ is one-one\\
(4) If $f \circ g$ is one-one, then $g$ is one-one

Paper Questions

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