Question

$f:Z\to Z$ and $f\left(x\right)=x^2$ then $f$ is

• A. a bijection
• B. a injection
• C. a surjection
• D. not a bijection

Answer 1

The correct option is D not a bijection

$f(-1)=f\left(1\right)=1$
Similarly $f(-\alpha )=f\left(\alpha \right)$ for all $\alpha \in N$
Hence $f$ is not one-one, hence not a bijection.
It is not a surijection as $f>0$, but co-domain is whole Z