JEE Mains · Maths · STD 12 - 1. relation and function
Let a function \(f: N \rightarrow N\) be defined by \(f ( n )=\left[\begin{array}{ll}2 n , \,\,\, \,\,\,\,\,\,n =2,4,6,8, \ldots . \\ n -1,\,\,\, n =3,7,11,15, \ldots . \\ \frac{ n +1}{2}, \,\,\, \,\,\,n =1,5,9,13, \ldots \ldots\end{array}\right.\) then, \(f\) is
- A one-one but not onto
- B onto but not one-one
- C neither one-one nor onto
- D one-one and onto
Answer & Solution
Correct Answer
(D) one-one and onto
Step-by-step Solution
Detailed explanation
\(f ( x )=\left\{\begin{array}{ccc}4 R ; n =2 R \\ 4 R -2 ; n =4 R -1 \\ 2 R -1 ; n =4 R -3\end{array}\right.\) \((R \in N)\) \(Note\) that for any element, it will fall into exactly. one of these sets. \(\{y: y=4 R ; y \in N\}\) \(\{y: y=4 R-2 ; y \in N\}\)…
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