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Retired Moderator Joined: 29 Apr 2015
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Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?

A. f(x) = $$x^2$$
B. f(x) = x + $$(x-1)^2$$
C. f(x) = x-1
D. f(x) = 5/x
E. f(x) = x/5

Please anyone explain how this works efficiently. I always struggle when I see these function questions. What do do first? Plug in what into what? At first I did not understand what the question wanted with f(x) with regards to f(y-z)= .... for me, this feels like reading chinese Note the phrasing of the question: "for all possible values of y and z". Only the right function will satisfy the condition for every possible value you choose; the other four answer choices may satisfy the condition for some values, but not for others.

Don't mess with the algebra, plug in easy numbers (for instance, z=1 and y=2) into each of the functions and POE. Keep plugging in and eliminate answer choices that do not meet the condition, until you are left with a single answer choice.

Plug in z = 1 and y = 2:

--> f(y-z) = f(2-1) = f(1) = 1-1 = 0

--> f(y) - f(z) = f(2) - f(1) = (2-1) - (1-1) = 1

Thus f(y-z) ≠ f(y) - f(z) for z=1 and y=2 and the answer is eliminated.

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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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reto wrote:
Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?

A. f(x) = x2
B. f(x) = x + (x-1)2
C. f(x) = x-1
D. f(x) = 5/x
E. f(x) = x/5

Please anyone explain how this works efficiently. I always struggle when I see these function questions. What do do first? Plug in what into what? At first I did not understand what the question wanted with f(x) with regards to f(y-z)= .... for me, this feels like reading chinese Note the phrasing of the question: "for all possible values of y and z". Only the right function will satisfy the condition for every possible value you choose; the other four answer choices may satisfy the condition for some values, but not for others.

Don't mess with the algebra, plug in easy numbers (for instance, z=1 and y=2) into each of the functions and POE. Keep plugging in and eliminate answer choices that do not meet the condition, until you are left with a single answer choice.

Plug in z = 1 and y = 2:

--> f(y-z) = f(2-1) = f(1) = 1-1 = 0

--> f(y) - f(z) = f(2) - f(1) = (2-1) - (1-1) = 1

Thus f(y-z) ≠ f(y) - f(z) for z=1 and y=2 and the answer is eliminated.

Please format your question properly. I think option A is $$x^2$$ and not x2.

Whenever you see function questions, more often than not, you will be able to solve the questions by plugging in. Also, you need to understand what do you mean by 'f(x)'. It means that there is a relationship in x that is satisfied by all values of x.

In the given question, you need to evaluate all the given f(x) such that f(y-z)=f(y)-f(z) for all y ,z (the underline portion means that the correct option HAS to be true for any set of values of y and z).

Now, look at the first option,

f(x) = $$x^2$$ (I am assuming that you wanted to write $$x^2$$)

Do not worry about the variable being x,y or z. You just need to realize that there is a functional connection between the variables.

Now, assume y=4 and z=3

f(4-3)=f(1)=1^2=1

and f(4)=16 (substitute x=4 in f(x) = $$x^2$$), f(3)=9 and f(4)-f(3) = 7 not equal to f(4-3). Thus this version of f(x) is incorrect. Repeat the same (with the same set of numbers) and you will see that only E remains.

More questions to practice: search.php?search_id=tag&tag_id=61
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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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The pick numbers strategy is probably the most efficient, so most should stick with that one. The theory behind it in layman's terms, since that's what I prefer, is that for each answer choice, plug whatever is in the function from the question stem where the variable $$x$$ is in the answer choice.

So for answer choice A. $$f(x)=x^{2}$$, plug $$(y-z)$$ into the equation (as though $$y-z$$ were $$x$$ itself) and perform the algebra. Therefore, since the functional notation is $$f(y-z) = f(y)-f(z)$$, the LHS is $$(y-z)^{2}$$ and the right hand side is $$y^{2} - z^{2}$$. The question is: are both sides equal? Not here, and therefore you must do the same for each answer. So replace $$x$$ with the variables of each function from the question $$(y-z)$$, $$y$$ and $$z$$ up until you find the equation where both sides are equal.

I found Magoosh has one of the better explanations of functional notation should you need a resource aside from gmatclub.
http://magoosh.com/gmat/2012/function-notation-on-the-gmat/

Thanks,
Intern  Joined: 12 Oct 2016
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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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Hi, i still don't understand this question. Could anyone plug in values in the E options to facilitate a better understanding.
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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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1
Swatipr wrote:
Hi, i still don't understand this question. Could anyone plug in values in the E options to facilitate a better understanding.

E. f(x) = x/5

Now for LHS x=y-z
so F(x) = F(y-z)
put x as Y-Z in X/5

f(y-z)=y-z/5= y/5-z/5---------1

similarly RHS

F(Y) = y/5---
F(Z)=Z/5 ---
F(Y)-F(Z)=Y/5 - Z/5------------2
we can se LHS =RHS ..so E remains.
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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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reto wrote:
Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?

A. f(x) = $$x^2$$
B. f(x) = x + $$(x-1)^2$$
C. f(x) = x-1
D. f(x) = 5/x
E. f(x) = x/5

Please anyone explain how this works efficiently. I always struggle when I see these function questions. What do do first? Plug in what into what? At first I did not understand what the question wanted with f(x) with regards to f(y-z)= .... for me, this feels like reading chinese :!:

Note the phrasing of the question: "for all possible values of y and z". Only the right function will satisfy the condition for every possible value you choose; the other four answer choices may satisfy the condition for some values, but not for others.

Don't mess with the algebra, plug in easy numbers (for instance, z=1 and y=2) into each of the functions and POE. Keep plugging in and eliminate answer choices that do not meet the condition, until you are left with a single answer choice.

Plug in z = 1 and y = 2:

--> f(y-z) = f(2-1) = f(1) = 1-1 = 0

--> f(y) - f(z) = f(2) - f(1) = (2-1) - (1-1) = 1

Thus f(y-z) ≠ f(y) - f(z) for z=1 and y=2 and the answer is eliminated.

-------------------

Just replace x by "y-z" on LHS while x by y & x by z in RHS
Plugging in these values will help realize that quadratic functions wont follow f(y-z) = f(y)-f(z), as the squaring of two combined terms will be different from individual squaring.
& similary with linear functions with a constant wont follow this due to the constant being nullified in subtractions & added in additions.

So the best type of function would be a linear function without a constant like y=kx
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Re: Which of the following functions f(x) satisfies the condition f(y-z) =  [#permalink]

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_________________ Re: Which of the following functions f(x) satisfies the condition f(y-z) =   [#permalink] 13 May 2019, 20:40
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