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If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.  [#permalink]

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New post 30 Oct 2017, 00:43
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

37% (01:21) correct 63% (01:32) wrong based on 87 sessions

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[GMAT math practice question]

If f(x+y) = f(x)f(y), which of followings can be the value of f(0)?

I. 0
II. 1
III. 2

A.I only
B. II only
C. III only
D. I and II only
E. I, II and III

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If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.  [#permalink]

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New post 30 Oct 2017, 08:39
1
1
MathRevolution wrote:
[GMAT math practice question]

If f(x+y) = f(x)f(y), which of followings can be the value of f(0)?

I. 0
II. 1
III. 2

A.I only
B. II only
C. III only
D. I and II only
E. I, II and III


at \(x=y=0\), we get

\(f(0)=f(0)*f(0) => f(0)={f(0)}^2\)

\({f(0)}^2-f(0)=0 =>f(0)[f(0)-1]=0\)

so \(f(0)=0\) or \(f(0)=1\)

Option D
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.  [#permalink]

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New post 01 Nov 2017, 00:57
1
=>

When we plug in x = 0 and y = 0, we have f(0) = f(0)f(0) or f(0)f(0) – f(0) = 0.
Then f(0){ f(0) – 1 } = 0, so we have f(0) = 0 or f(0) = 1.

Therefore, D is the answer.

Answer: D
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Re: If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.  [#permalink]

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New post 27 Nov 2017, 13:53
MathRevolution wrote:
[GMAT math practice question]

If f(x+y) = f(x)f(y), which of followings can be the value of f(0)?

I. 0
II. 1
III. 2

A.I only
B. II only
C. III only
D. I and II only
E. I, II and III


f(0) = f(0+0) = f(0)f(0)
= f(0)=f(0)^2
= f(0)- f(0)^2 = 0
= f(0) (1-f(0)) = 0
= f(0)= 0 and f(0) = 1; D.
GMAT Club Bot
Re: If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I. &nbs [#permalink] 27 Nov 2017, 13:53
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If f(x+y) = f(x)f(y), which of followings can be the value of f(0)? I.

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