Excluded values. why is it necessary to give these values in simplified rational expression.?

Question

Excluded values are an attempt to solve for a variable to make the denominator zero. this is the answer I gave but my teacher said I needed more clarifacation.

this is the question she asked me directly in class

Throughout this Unit we have reminded you that sometimes answers are not correct for all values of a variable. The values not included are called “excluded values”. Why do you think it is necessary to give the “excluded values” when you write your answers to a simplified rational expression? Think about this question and write your thoughts in the space below.

Answer 1

Suppose you have the rational function f(x)=x²/x. It is clear that this function can be simplified to f(x)=x and that this function will have the same value as the original function everywhere divixion by x is defined.

Pay attention to that last point: everywhere division by x is defined. If x=0, the first funciton gives you 0/0 which is NOT defined. As such, the domain of the first function does not include zero, because it doesn't give you an answer for x=0. However, the simplified function does include x=0 in its domain, and gives the answer 0. That means that these two are not the same function, because one contains zero in its domain and the other does not. To make them the same function, we must explicitly exclude 0 from the domain of the second function, which is why, in this case, you would write zero as an excluded value.

Your teacher was being very lenient: your answer was not merely badly explained, it was wrong. While it is true that the values you exclude in this case are precisely those where the denominator is zero, the purpose of excluded values is not to make the denominator zero, but to make sure that the denominator is not zero within the domain of the function (which is why you are excluding these values from the domain of the function).

Answer 2

In math, all answers should be given in their simplest form including the excluded values.

Answer 3

which values specifically are you referring to?

Answer 4

can you give a specific example?

Answer 5

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