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

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

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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.)
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CEO
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04 Jun 2007, 12:56

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
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04 Jun 2007, 14:31
OA: E
That helps...... Thanks!

Manager
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06 Jun 2007, 13:25
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.
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06 Jun 2007, 13:31
went from A to E too
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06 Jun 2007, 13:32
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 ?
06 Jun 2007, 13:32
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