is there a difference between the function y=x/x and the function y=1.

Question

I have been asking people and have been getting mixed answers. some people think it is the same because when you simplify the first one you get y=1, but some people think that they are different because in the first equation x cannot be 0, and in the second equation x can be 0. Please tell me.

Answer 1

An expression alone is not a function. A function needs to have a domain specified. On the domain $\Bbb R\setminus \{0\}$ (or any subset thereof), they are the same function. On the domain $\Bbb R$, $\frac xx$ is not a function.