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Let the function g(a, b) = f(a) + f(b).

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Let the function g(a, b) = f(a) + f(b). [#permalink] New post 29 Nov 2012, 18:17
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Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?

A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4
[Reveal] Spoiler: OA

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Last edited by Bunuel on 30 Nov 2012, 01:41, edited 1 time in total.
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Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 29 Nov 2012, 21:55
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gmatbull wrote:
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?

A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4

OA to be posted later.


The question is basically asking for which function f(a + b) = f(a) + f(b)

A)LHS = a + b + 3
RHS = a + 3 + b + 3 = a + b + 6.
Not equal

B)LHS = (a + b)^2
RHS = a^2 + b^2
Not equal

C)LHS = |a + b|
RHS = |a| + |b|
If a & b are of different polarity not equal.

D)LHS = \frac{1}{a + b}
RHS = \frac{1}{a} + \frac{1}{b}
Not equal

E)LHS = \frac{a + b}{4}
RHS = \frac{a}{4} + \frac{b}{4} = \frac{a + b}{4}.
Equal.

Answer should be E
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Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 30 Nov 2012, 02:02
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Expert's post
Let the function g(a, b) = f(a) + f(b).

For which function f below will g(a + b, a + b) = g(a, a) + g(b, b)?


A: x +3
B: x^2
C: |x|
D: 1/x
E: x/4

We can use plug-in method to solve this question.

Since g(a, b) = f(a) + f(b), then:
g(a + b, a + b)=f(a+b)+f(a+b)=2f(a+b);
g(a, a) + g(b, b)=f(a)+f(a)+f(b)+f(b)=2f(a)+2f(b).

Thus the question asks: for which function f below will 2f(a+b)=2f(a)+2f(b) --> f(a+b)=f(a)+f(b)?

Say a=-1 and b=1, then the question becomes: for which function f below will f(0)=f(-1)+f(1).

A: x +3
f(0)=0+3=3
f(-1)+f(1)=(-1+3)+(1+3)=6
No match.

B: x^2
f(0)=0^2=0
f(-1)+f(1)=(-1)^2+(1)^2=2
No match.

C: |x|
f(0)=|0|=0
f(-1)+f(1)=|-1|+|1|=2
No match.

D: 1/x
f(0)=\frac{1}{0}=undefined
f(-1)+f(1)=\frac{1}{-1}+\frac{1}{1}=0
No match.

E: x/4
f(0)=\frac{0}{4}=0
f(-1)+f(1)=\frac{-1}{4}+\frac{1}{4}=0
Match.

Answer: E.

Hope it's clear.

for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html
functions-problem-need-help-93184.html

Hope it helps.
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Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 30 Nov 2012, 02:52
Bunuel and MacFauz,
your explanations make a lot of sense.
More so, Bunuel, you took time to explain the breakdown.

Thanks.
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Re: Let the function g(a, b) = f(a) + f(b). [#permalink] New post 23 Jul 2013, 01:15
Expert's post
Re: Let the function g(a, b) = f(a) + f(b).   [#permalink] 23 Jul 2013, 01:15
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