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Question

If f:{1,3,4}C, where C is the co-domain of the function and f(x)=x23x+2, then the co-domain of the function can be
  1. Set of first 10 whole numbers
  2. Set of factors of 6
  3. Set of even integers
  4. Set of natural numbers


Solution

The correct options are
A Set of first 10 whole numbers
C Set of even integers
Since, function is defined as f:{1,3,4}C, the image of each and every element of {1,3,4} should be in C.
f(1)=(1)23(1)+2=0
f(3)=(3)23(3)+2=2
f(4)=(4)23(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{0,1,2,3,4,5,6,7,8,9}

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

Set of even integers is {0,±2,±4,±6,...}
0,2,6{0,±2,±4,±6,...}

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

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