Question

If A = (-2, -1, 0, 1, 2) and f : A → B is a surjection defined by f(x) = x² + x + 1 then find B.

Answer 1

Answer:

Codomain , B = {1,3,7}

Step-by-step explanation:

In the attachment I have answered this problem.

See the attachment for detailed solution.

I hope this answer helps you

Answer 2

Solution:

If A is a finite set defined defined as A = (-2, -1, 0, 1, 2)

and a function f:A → B is such that

f(x) = x² + x + 1

if f(x) is surjective than B must be a set like every element of a has an image in B

So,put each value of A in the function

$f( - 2) = ( { - 2)}^{2} + ( - 2) + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 - 2 + 1 \: = > 3 \\ \\ f( - 1) = ( { - 1)}^{2} + ( - 1) + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 - 1+ 1 \: = > 1 \\ \\ f(0) = ( { 0)}^{2} + ( 0) + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 0+ 0 + 1 \: = > 1 \\ \\ f( 1) = ( { 1)}^{2} + ( 1) + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 + 1 + 1 \: = > 3 \\ \\ f(2) = ( { 2)}^{2} + ( 2) + 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 + 2 + 1 \: = > 7$
So the set B = {1,1,3,3,7}

and we know that repetition is not allowed in Set

So B ={1,3,7}

Hope it helps you .