Step1: Injective or One-One function:

Let $f:R \to R$ and

$f(x)=x^2$

let x1 =-1 and x2=1 be two elements in R

$f(-1)=f(1)\; since\; (-1)^2 =(1)^2$

but $-1 \neq 1$

$f : R\to R \;given\; by\; f(x)\; = x^2$ is not injective as f(x1) =f(x2) does not imply x1=x2

Step 2: Surjective or On-to function:

Let $f:R \to R$ and

Let us consider the element -2 , for $-2 \in R $ there does not exists $ x \in R$ such that $f(x)=x^2=-2$

$\sqrt {-2} \notin Z$

$f : R\to R \;given\; by\; f(x)\; = x^2$ is not surjective as for every $y\in R$ there does not exist $x\in R $ such that f(x)= y

Solution:Hence$f : R\to R \;given\; by\; f(x)\; = x^2$ is neither injective nor surjective