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For which of the following functions f(x) is f(a + b) = f(a)

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GMAT Club Legend
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For which of the following functions f(x) is f(a + b) = f(a) [#permalink] New post 30 Jul 2018, 09:42
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Question Stats:

57% (00:57) correct 42% (03:41) wrong based on 7 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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Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink] New post 05 Aug 2018, 09:14
Have just resolved it, the solution is B. Is there anybody has another solution?
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Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink] New post 06 Aug 2018, 09:12
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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
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GMAT Club Legend
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Re: For which of the following functions f(x) is f(a + b) = f(a) [#permalink] New post 12 Aug 2018, 07:06
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
Capture.PNG [ 457.02 KiB | Viewed 301 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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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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