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

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

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New post 06 Jan 2019, 23:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

43% (00:58) correct 57% (01:29) wrong based on 42 sessions

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[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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New post 07 Jan 2019, 00:10
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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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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)?  [#permalink]

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New post 07 Jan 2019, 01:07
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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New post 07 Jan 2019, 01:47
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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New post 07 Jan 2019, 02:17
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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New post 07 Jan 2019, 03:29
fighterboy wrote:
Thanks a lot! I understood the logic.

Alternate explanation:

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

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Fabio.
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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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New post 09 Jan 2019, 00:19
=>

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 \(f(1) = 0.\)

Therefore, the answer is C.
Answer: C
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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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New post 09 Jan 2019, 10:33
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
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Re: If f(a*b) = f(a) + f(b), what is the value of f(1)? &nbs [#permalink] 09 Jan 2019, 10:33
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