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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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For which of the following functions f(x) is f(a + b) = f(a) [#permalink]
Expert's post 00:00

Question Stats: 60% (00:46) correct 40% (03:13) wrong based on 10 sessions
For which of the following functions f(x) is $$f(a + b) = f(a) + f(b)$$?

(A) $$f(x) = x^2$$
(B) $$f(x) = 5x$$
(C) $$f(x) = 2x + 1$$
(D) $$f(x) =\sqrt{x}$$
(E) $$f(x) = x - 2$$
[Reveal] Spoiler: OA

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Sandy
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Intern Joined: 05 Aug 2018
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Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink]
Have just resolved it, the solution is B. Is there anybody has another solution? GRE Instructor Joined: 10 Apr 2015
Posts: 1550
Followers: 56

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Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink]
1
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Expert's post
sandy wrote:
For which of the following functions f(x) is $$f(a + b) = f(a) + f(b)$$?

(A) $$f(x) = x^2$$
(B) $$f(x) = 5x$$
(C) $$f(x) = 2x + 1$$
(D) $$f(x) =\sqrt{x}$$
(E) $$f(x) = x - 2$$

One approach is to let a = 1 and b = 1 and plug in the values.

So, the question becomes, "Which of the following functions are such that f(1 + 1) = f(1) + f(1)?"
In other words, for which function does f(2) = f(1) + f(1)?

A) If f(x) = x², does f(2) = f(1) + f(1)?
Plug in to get: 2² = 1² + 1²
No, doesn't work
So, it is not the case that f(2) = f(1) + f(1), when f(x) = x²
ELIMINATE A

B) If f(x) = 5x, does f(2) = f(1) + f(1)?
Plug in to get: 5(2) = 5(1) + 5(1)
It works. KEEP B for now.

C) If f(x) = 2x + 1, does f(2) = f(1) + f(1)?
Plug in to get: 2(2) + 1 = 2(1) + 1 + 2(1) + 1
No, doesn't work
So, it is not the case that f(2) = f(1) + f(1), when f(x) = 2x + 1
ELIMINATE C

D) If f(x) = √x, does f(2) = f(1) + f(1)?
Plug in to get: √2 = √1 + √1
No, doesn't work
So, it is not the case that f(2) = f(1) + f(1), when f(x) = √x
ELIMINATE D

E) If f(x) = x - 2, does f(2) = f(1) + f(1)?
Plug in to get: 2 - 2 = (1 - 2) + (1 - 2)
No, doesn't work
So, it is not the case that f(2) = f(1) + f(1), when f(x) = x - 2
ELIMINATE E

By the process of elimination, the correct answer is B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails

GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink]
Expert's post
Explanation

The question asks which of the functions in the answer choices is such that performing the function on a + b yields the same answer as performing the function to a and b individually and then adding those answers together.

The correct answer should be such that f(a + b) = f(a) + f(b) is true for any values of a and b. Test some numbers, for example a = 2 and b = 3:

Attachment: Capture.PNG [ 457.02 KiB | Viewed 657 times ]

Alternatively, use logic—for what kinds of operations are performing the operation on two numbers and then summing results the same as summing the original numbers and then performing the operation?

Multiplication or division would work, but squaring, square-rooting, adding, or subtracting would not. The correct function can contain only multiplication and/or division.
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Sandy
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Try our free Online GRE Test Re: For which of the following functions f(x) is f(a + b) = f(a)   [#permalink] 12 Aug 2018, 07:06
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