Question

If $A=\{-2,-1,0,1,2\}$ and $f:A$ $\to$ $B$ is a surjection defined by $f\left(x\right)=$ $x^2+x+1$, then find $B$.

Answer 1

$A=\{-2,-1,0,1,2\}$

Given f(x)$=x^2+x+1$ from A$\to$ B

$f(-2)=(-2{)}^2-2+1=3$

$f(-1)=(-1{)}^2-1+1=1$

$f\left(0\right)=(0{)}^2+0+1=1$

$f\left(1\right)=(1{)}^2+(1)+1=3$

$f\left(2\right)=2^2+2+1=7$

$B=\{3,1,7\}$