Question

请教一道离散数学题

Is the function f: Z→Z defined as f(n) = n^2 +1 one-to-one? Explain.

Answer 1

f is not one-to-one

choose 2∈升昌蔽吵州迅坦Z, then we can find tow members of Z , -1 and 1 ,such that

f(-1)=f(1) = 2

so f is not into

therefor f is not one to one

Answer 2

并非one-to-one，即不是一一对应的关系

因为f是整数到睁闭整数的映射

n和猛雀-n在f作用下都映射到n^2+1

故不是一一映射枝早早

The function f is not one-to-one, because n and -n will be cast to n^2+1 by fuction f in the range of integer