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

There are piecewise functions that have names, but you can’t really go from the piecewise definition to the named function without knowing what it is. For example, there’s no algebraic way to go from f(x) = {-x for x<0, x for x>=0} to f(x) = absolute value of x, but they’re the same function by definition.