Answer by Julio Puerta for Rational functions where they are undefined
In fact, $f_1(x)\cdot f_2(x)=\dfrac{x-5}{x-5}$ is not the same function as $f_3(x)=1$.One has that $f_1(x)\cdot f_2(x)=1=f_3(x)$ for every $x\neq 5$, but in $x=5$$f_1\cdot f_2$ is not defined as the...
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Rational functions where they are undefined
There's something I can't quite wrap my head around, and I am not satisfied with my professor's "that's just defined that way" answer. So suppose we have:$$f_1(x) = x - 5$$$$f_2(x) = \frac{1}{x -...
View ArticleAnswer by fleablood for Rational functions where they are undefined
Another way of looking at it other than Julio Puerta's excellent answer is to realize that the domain of function is an essential part of the definition of a function and can not be ignored.So the...
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