Do any two different functions exist that cannot be simplified to the same form but generate the same graph?

Question

Do any two different functions exist that cannot be simplified to the same form but generate the same graph?

In: Mathematics

Answer 1

Yes, there are, but I can not give you an example.  You can show that there are theorms that are true but impossible to prove.  You could take a function that is equal to 1 iff such a theorm is true for some value. This function is equal to 1, but you can not show that.