Domain of a function

[jasoncurious]

Hi all, there's this function:

 

y=(x^2-6*x+5)/(x-1) which can be reduced to y=(x-5)(x-1)/(x-1) and then to y=x-5

 

The question asked me to determine the domain and range of this function. Here's the problem, when the function is y=(x^2-6*x+5)/(x-1), the domain is every real number except 1. But when it's been reduced to y=x-5, the domain should be every real number. However, the answer stated that the domain is still every real number except 1.

 

How should I solve this problem?

Edited December 15, 2012 by jasoncurious

[ajb]

This is a technicality, but the domain of the two functions you give, a rational function and its reduction are different. By reduction you have removed the "division by zero" problem.

 

I think it is now an issue of convention as to what you state as the domain. It looks like your book (or teacher) is considering the domain before reduction. Thus you get all values except x=1.

[jasoncurious]

Thanks, so I assume this type of to be contextual?

[ajb]

Thanks, so I assume this type of to be contextual?

Yes, it is contextual and partly an issue of conventions.