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

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For which of the following functions is f(a + b) = f(a) [#permalink]

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New post 14 Oct 2008, 17:15
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

For which of the following functions is f(a + b) = f(a) +f(b) for all positive numbers a and b.

a. f(x) = x^2
b. f(x) = x + 1
c. f(x) = sqrt x
d. f(x) = 2/x
e. f(x) = -3x

Thanks!

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Re: Function Question [#permalink]

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New post 14 Oct 2008, 17:34
E

-3a + (-3b) = -3(a+b)

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Re: Function Question [#permalink]

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New post 22 Oct 2008, 17:24
The answer is e but I'm still having trouble understanding this. Can someone please explain this in more detail.

Thanks.

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Re: Function Question [#permalink]

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New post 22 Oct 2008, 19:14
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Poots wrote:
The answer is e but I'm still having trouble understanding this. Can someone please explain this in more detail.

Thanks.


what you are trying to do here is check how f(a+b) would be equal to f(a) + f(b)

ie insert this in all your choices

is (x+y) ^2 = x^2 + y^2 ?....no
is (x+y+1) = x+1 + y+h....no
.
.
.
.
-3(x+y) = -3x + (-3)y

Hence E...i hope this helps

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Re: Function Question [#permalink]

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New post 23 Oct 2008, 05:06
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Poots wrote:
For which of the following functions is f(a + b) = f(a) +f(b) for all positive numbers a and b.

a. f(x) = x^2
b. f(x) = x + 1
c. f(x) = sqrt x
d. f(x) = 2/x
e. f(x) = -3x

Thanks!


Poots wrote:
The answer is e but I'm still having trouble understanding this. Can someone please explain this in more detail.

Thanks.


Poots.. you can pick up two numbers.. say 2 and 3 (lets keep it simple)

a. f(x) = x^2 ------ f(2+3) = 5² = 25 which is NOT equal to f(2) + f(3) = 2² + 3² = 13 ----- (25 !=13)
b. f(x) = x + 1
c. f(x) = sqrt x
d. f(x) = 2/x
e. f(x) = -3x

when we try for all the choices we see that only choice E holds good.

f(2+3) = -3(2+3) = -15
f(2) + f(3) = [-3(2)] + [-3(3)] = -6 - 9 = -15
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Re: Function Question [#permalink]

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New post 23 Oct 2008, 18:49
Math is the type of thing I really need broken down.

Thank you all for all your help.

Your explanations helped me to my epiphany.

--Poots

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Re: Function Question [#permalink]

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New post 23 Oct 2008, 18:55
Poots wrote:
Math is the type of thing I really need broken down.

Thank you all for all your help.

Your explanations helped me to my epiphany.

--Poots


:lol: epiphany
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Re: Function Question   [#permalink] 23 Oct 2008, 18:55
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For which of the following functions is f(a + b) = f(a)

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