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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7501
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If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 43% (01:07) correct 57% (00:55) wrong based on 59 sessions

HideShow timer Statistics [Math Revolution GMAT math practice question]

If $$f(a*b) = f(a) + f(b)$$, what is the value of $$f(1)$$?

$$A. 1$$
$$B. -1$$
$$C. 0$$
$$D. 2$$
$$E. -2$$

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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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1
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$f(a*b) = f(a) + f(b)$$, what is the value of $$f(1)$$?

$$A. 1$$
$$B. -1$$
$$C. 0$$
$$D. 2$$
$$E. -2$$

Let a = b= 1. We have -
f(1) = 2f(1)

f(1) = 0.
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Joined: 02 Dec 2017
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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I got answer as 2, can anybody explain me how?
rahul16singh28 I didn't understand the logic of 2f(1)=0
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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fighterboy,

If f(1) is not equal to zero , then
f(1) = 2f(1) - Dividing both sides by f(1)
1=2 , which is not possible

Hence f(1) must be zero
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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Thanks a lot! I understood the logic.
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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fighterboy wrote:
Thanks a lot! I understood the logic.

Alternate explanation:

$$f\left( 1 \right) = 2 \cdot f\left( 1 \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,2 \cdot f\left( 1 \right) - f\left( 1 \right) = 0\,\,\,\,\, \Rightarrow \,\,\,\,f\left( 1 \right) = 0$$

Regards,
Fabio.
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Math Revolution GMAT Instructor V
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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=>

Since $$1 = 1 * 1$$, setting $$a = 1$$ and $$b = 1$$ yields $$f(1) = f(1*1) = f(1) + f(1)$$ and $$f(1) = 2f(1),$$ which is equivalent to $$f(1) = 0.$$

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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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Given f(a*b)=f(a)+f(b)
Let a = b= 1. We have -
f(1*1) = f(1)+f(1)
f(1)=2f(1)
2f(1)-f(1)=0
Hence, f(1)=0 Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?   [#permalink] 09 Jan 2019, 11:33
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