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# My apologies if this is a repost: For which of the

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Intern
Joined: 30 Nov 2006
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My apologies if this is a repost: For which of the [#permalink]  04 Jun 2007, 10:59
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My apologies if this is a repost:

For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers of a and b?
(please refer to the attached file.)
Attachments

PS - f(x).JPG [ 12.56 KiB | Viewed 379 times ]

CEO
Joined: 17 May 2007
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I arrive this by elimination. Unfortunately I went from A to E so it took me the longest.

But its easy to eliminate A and C
(a+b)^2 not equal to a^2 + b^2
and
sqrt(a+b) not equal to sqrt(a)+sqrt(b)

Then we eliminate B and D
(a+b+1) is not equal to (a+1)+(b+1) (simplified to a+b+2)
and
2/(x+y) is not equal to 2/x + 2/y (simplified to (2x + 2y)/xy )

You can do the maths yourself to see E is indeed always true
Intern
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OA: E
That helps...... Thanks!

Manager
Joined: 14 Mar 2007
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For starters:
The qus says f(a+b)=f(a)+f(b)

So when we take up a choice
f(x)=x^2
where does the f(a)+f(b) go.
Hope this is not too basic.
Director
Joined: 13 Mar 2007
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went from A to E too
CEO
Joined: 17 May 2007
Posts: 2994
Followers: 59

Kudos [?]: 467 [0], given: 210

OH I see...

If f(x) is x^2 that simply implies that f(a) is a^2 and that f(b) is b^2 and similarly F(a+b) is (a+b)^2 ... this can be simplified to a^2 + b^2 + 2*a*b

so f(a) + f(b) = a^2 + b^2 which is NOT same as f(a+b) which is a^2 + b^2 + 2*a*b

Does this make it any clearer ? Anything else I can clarify here ?
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Repost 1 01 Mar 2014, 13:12
My apologies (again) if this is a re-post: It's a 6 04 Jun 2007, 11:13
The Dean of the College accepted my apologies for the way 18 06 Sep 2006, 15:32
My apologies if this has already been posted. Mr. Janeck: I 7 08 Sep 2005, 10:39
this is a repost from my last time...still made the same 3 31 May 2005, 08:04
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