Question

Let $f:Z$ $\to$ $Z$ be defined as f(x) $=x^2,x\in Z$. $f$ is

• A. a bijection
• B. an injection
• C. a surjection
• D. a function

Answer 1

The correct option is D a function

Let $f:Z\mapsto Z$ be defined as $f\left(x\right)=x^2,x\in Z$.

We know that the square of an integer is always a unique integer.

So, ''$f$'' is a function.
Now, since $f(-2)=f\left(2\right)=4$, ''$f$'' is not an injection.
There is no integer $x\in Z:f\left(x\right)=-1$.

Hence , ''$f$'' is not a surjection.
Since ''$f$'' is neither one-one nor onto, ''$f$'' is not a bijection.