Question

If $f:\{1,3,4\}\to C$, where $C$ is the co-domain of the function and $f\left(x\right)=x^2-3x+2$, then the co-domain of the function can be

• A. Set of first $10$ whole numbers
• B. Set of factors of $6$
• C. Set of even integers
• D. Set of natural numbers

Answer 1

Answer: (A), (C)

Set of even integers

Since, function is defined as $f:\{1,3,4\}\to C$, the image of each and every element of $\{1,3,4\}$ should be in $C$.
$f\left(1\right)=(1{)}^2-3(1)+2=0$
$f\left(3\right)=(3{)}^2-3(3)+2=2$
$f\left(4\right)=(4{)}^2-3(4)+2=6$
So, co-domain can be any set consisting $0,2,6$ as their elements.

Set of first $10$ whole numbers is $\{0,1,2,3,4,5,6,7,8,9\}$
$0,2,6\in \{0,1,2,3,4,5,6,7,8,9\}$

Set of factors of $6$ is $\{1,2,3,6\}$
$0\notin \{1,2,3,6\}$

Set of even integers is $\{0,\pm 2,\pm 4,\pm 6,...\}$
$0,2,6\in \{0,\pm 2,\pm 4,\pm 6,...\}$

Set of natural numbers is $\{1,2,3,4,...\}$
$0\notin \{1,2,3,4,...\}$