Re: Among the following functions, for which one is

Here is how I approached this. Since I have been pretty weak with function for close to 15 odd years now and find it helpful to see more detailed steps , please bear with my answer here!

Since we want g(x-y) = g(x) - g(y) for all the answer options below, replace x with (x-y) and see if the RHS can give us a function in the form of [g(x)-g(y)]

A. g(x-y)= (x-y)^4 This would not give us the result in the required form once you simplify. PS - I didn't think we need to actually simplify here to make this observation

B. g(x-y) = (x-y)-7 This does not give us the result in the required form once you simplify because of the additional 7 (Oh so close!) .

C. g(x-y) = \sqrt{(x-y)+3}[/b] This would not give us the result in the required form once you simplify. PS - I didn't think we need to actually simplify here to make this observation

D. g(x-y)= \frac{4}{[(x-y)-4]} This would not give us the result in the required form once you simplify. PS - I didn't think we need to actually simplify here to make this observation

E. g(x-y) = 7(x-y)
=7x - 7y
= g(x) - g(y) OA for this problem