Abstract Algebra Question: Let R be an equivalence relation on the set of real differentiable functions defined by fRg iff f and g has the same first derivative, i.e. f' = g'. Determine the equivalence classes of f for each f element of R.

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The equivalence class of f would just be the set of functions such that every function in the set is equal to f plus a constant term (The derivative of a constant term is 0).

so should i define f. that means should i specify f in order to find the classes?

f is just a real differentiable function. The most important thing is to define what a constant is. In this case, you should define the constant by saying it's a continuous differentiable function such that it's first derivative is 0.

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