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Re: Among the following functions, for which one is [#permalink]
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!) :twisted: .

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
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Re: Among the following functions, for which one is [#permalink]
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Hi All,

This prompt is remarkably similar in design to the following question (and it can be solved in the same ways that this question is solved):

for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html

GMAT assassins aren't born, they're made,
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Re: Among the following functions, for which one is [#permalink]
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guerrero25 wrote:
Among the following functions, for which one is g(x − y) = g(x) − g(y) for all values of x and y in the domain of y?


(A)g(a)= a^{4}
(B) g(a)= a-7
(C)g(a)=sqrt{a+3}
(D) g(a)={4}/{a-4}
(E) g(a)=7a


take the function g as distributive law that we learnt in class fifth!! Then clearly option E satisfies. Hence E. Cant apply distributive laws on the other options :D

By the way... distributive law is a(x+y) = ax+ay. Similarly a(x-y) = ax-ay

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Re: Among the following functions, for which one is [#permalink]
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guerrero25 wrote:
Among the following functions, for which one is g(x − y) = g(x) − g(y) for all values of x and y in the domain of y?


(A) g(a)= a^{4}
(B) g(a)= a-7
(C) g(a)=sqrt{a+3}
(D) g(a)={4}/{a-4}
(E) g(a)=7a


Check functions related questions in our Special Questions Directory.

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re: Among the following functions, for which one is [#permalink]
aah man, why did I not start with testing E first? :D
7(x-y) = 7x - 7y
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Re: Among the following functions, for which one is [#permalink]
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Re: Among the following functions, for which one is [#permalink]
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