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TS EAMCET · Maths · Functions

If \(f: Z \rightarrow N\) is defined by \(f(n)=\left\{\begin{array}{cll}2 n, & \text { if } & n>0 \ 1, & \text { if } & n=0, \text { then } f \text { is } \ -2 n-1, & \text { if } & n < 0\end{array}\right.\)

  1. A one-one but not onto
  2. B onto but not one-one
  3. C both one-one and onto
  4. D neither one-one nor onto
Verified Solution

Answer & Solution

Correct Answer

(B) onto but not one-one

Step-by-step Solution

Detailed explanation

We have, \(f(n)= \begin{cases}2 n, & \text { if } n>0 \\ 1, & \text { if } n=0 \\ -2 n-1, & \text { if } n 0\) \(f(n)=2,4,6,8 \ldots .\) When, \(n < 0\) \(f(n)=1,3,5,7 \ldots . .\) \(\therefore\) Range of \(f(n)\) is \(\{1,2,3,4, \ldots .\).\(\} .\) \(\therefore \quad\) Codomain…