Among the following functions, for which one is

Question

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

blueseas · Answer

(A) g(a)= a^4 
put x= 1 y= 1 
 g(1-1)= 0^4 =0  and  g(1)+g(1) = 2 
hence no

(B)  g(a)= a-7 
put x= 1 y= 1 
 g(1-1)=-6  and  g(1)+g(1) = -12 
no

(C) g(a)=\sqrt{{a+3}} 
put  x= 1 y= 1 
 g(1-1)=  \sqrt{3} and  g(1)+g(1) = 4 
no

(D)  g(a)=\frac{{4}}{{a-4}} 
put  x= 1 y= 1 
 g(1-1)=  -1 AND g(1)+g(1) =-8/3 
no

E) g(a)=7a 
put  x= 1 y= 1 
 g(1-1)=0 AND g(1)+g(1) =0 
yes
hence E

Asifpirlo · Answer

................. i was lucky that i started from the reverse order and found the 1st (E) as the solution :-D

MBAjunkie16 · Answer

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 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} 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}{ } 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

EMPOWERgmatRichC · Answer

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,
Rich

sagarsir · Answer

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

Kudos.. if it helps :D

Bunuel · Answer

Check functions related questions in our  Special Questions Directory .

Operations/functions defining algebraic/arithmetic expressions 
 Symbols Representing Arithmetic Operation 
 Rounding Functions 
 Various Functions

mvictor · Answer

aah man, why did I not start with testing E first? :D
7(x-y) = 7x - 7y

bumpbot · Answer

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Among the following functions, for which one is

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Among the following functions, for which one is

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