Maths · One-one, into and onto functions
Let be the set of integers and be defined as =\boldsymbol{x}^{2}, \boldsymbol{x}
Let \( \mathbb{Z} \) be the set of integers and \( \boldsymbol{f}: \mathbb{Z} \rightarrow \) \( \mathbb{Z} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{x} \in \mathbb{Z} \) then function is
- A. bijection
- B. injection
- C. surjection
- D. none of these
Step-by-step solution
The function f(x)=x^2 from integers to integers is not injective because f(-1)=f(1)=1, and not surjective because negative integers have no preimage. Hence it is neither bijective, injective, nor surjective.
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