Suppose [tex] f(x) = \frac{x^2 - 1}{x-1} [/tex]. Why do we say that [tex] f(x) = \frac{x^2 - 1}{x-1} = x + 1 [/tex], if [tex]\frac{x^2 - 1}{x-1}[/tex] isn't defined at x = 1, but (x + 1) is defined at x = 1.
I always thought that we say two functions are equal to each other if their equations are the same and their domain is the same.
I always thought that we say two functions are equal to each other if their equations are the same and their domain is the same.