In the equation f(x)=1/2x if the range is a whole number what is the domian.

Expert Answers
embizze eNotes educator| Certified Educator

Given the equation `f(x)=1/2 x ` , we are told that the range is a whole number.

Thus the output from the function is a whole number. In order for the output to be a whole number, the input must have been even.

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The domain of the function is an even number

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If the range was whole numbers, then the domain would be even whole numbers. If the range was integers, then the domain would be even integers.

nick-teal eNotes educator| Certified Educator

I think the question is looking for is for you to recognize that the domain will be 2x the range.  If the range is 4 (-2 , 2) then the domain will be 8 (-4 , 4).

And because 2 times any whole number is even, the domain will always be even.

gsenviro eNotes educator| Certified Educator

For the given equation, f(x) = 1/2x , it is given that the range is a whole number, i.e. f(x) is a whole number and for that to happen, x must be an even whole number. Thus, the domain of the function is "even whole number".