Maths · One-one, into and onto functions
Let defined by = \) then is.
Let \( f: N \rightarrow N \) defined by \( f(n)= \) \( \left\{\begin{array}{cc}\frac{n+1}{2} & \text { if } n \text { is odd } \\ \frac{n}{2} & \text { if } n \text { is even }\end{array}\right. \) then \( \boldsymbol{f} \) is.
- A. Many-one and onto
- B. One-one and not onto
- C. onto but not one-one
- D. Neither one-one nor onto
Step-by-step solution
f(n) = ceil(n/2) maps both 1 and 2 to 1, so not one-one. For any m in N, f(2m)=m, so onto. Hence many-one and onto.
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