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# The function f is defined by f(x)=-1/x for all nonzero numbers x. If

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Joined: 03 Feb 2017
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The function f is defined by f(x)=-1/x for all nonzero numbers x. If  [#permalink]

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Updated on: 21 Sep 2018, 21:00
1
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Difficulty:

35% (medium)

Question Stats:

62% (00:36) correct 38% (00:37) wrong based on 13 sessions

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The function f is defined by f(x)=-1/x for all nonzero numbers x. If f(a)=-1/2 and f(ab)=1/6, then b=

A) 3
B) 1/3
C) -1/3
D) -3
E) -12

Originally posted by janchang on 21 Sep 2018, 14:38.
Last edited by chetan2u on 21 Sep 2018, 21:00, edited 1 time in total.
Moved to correct forum and added OA
Math Expert
Joined: 02 Aug 2009
Posts: 7971
The function f is defined by f(x)=-1/x for all nonzero numbers x. If  [#permalink]

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21 Sep 2018, 20:58
janchang wrote:
The function f is defined by f(x)=-1/x for all nonzero numbers x. If f(a)=-1/2 and f(ab)=1/6, then b=

A) 3
B) 1/3
C) -1/3
D) -3
E) -12

$$f(x)=\frac{-1}{x}$$...
So $$f(a)=\frac{-1}{a}$$=$$\frac{-1}{2}$$, so a=2
$$f(ab)=\frac{-1}{ba}$$=$$\frac{1}{6}$$, so ba=-6..
But a=2, so b*2=-6......b=-3

D
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Re: The function f is defined by f(x)=-1/x for all nonzero numbers x. If  [#permalink]

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21 Sep 2018, 21:19
janchang wrote:
The function f is defined by f(x)=-1/x for all nonzero numbers x. If f(a)=-1/2 and f(ab)=1/6, then b=

A) 3
B) 1/3
C) -1/3
D) -3
E) -12

OA: D

$$f(x)=-\frac{1}{x}$$ for all nonzero numbers $$x$$

$$f(a)=-\frac{1}{a}=-\frac{1}{2}$$

$$a= 2$$

$$f(ab)=-\frac{1}{ab}=\frac{1}{6}$$.......(1)

Putting $$a= 2$$ in $$(1)$$, we get

$$-\frac{1}{2b}=\frac{1}{6}$$

$$b=-3$$
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: The function f is defined by f(x)=-1/x for all nonzero numbers x. If  [#permalink]

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22 Sep 2018, 02:27
janchang wrote:
The function f is defined by f(x)=-1/x for all nonzero numbers x. If f(a)=-1/2 and f(ab)=1/6, then b=

A) 3
B) 1/3
C) -1/3
D) -3
E) -12

Discussed here: https://gmatclub.com/forum/the-function ... 09347.html

TOPIC IS LOCKED AND ARCHIVED.
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Re: The function f is defined by f(x)=-1/x for all nonzero numbers x. If  [#permalink]

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07 Oct 2019, 00:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The function f is defined by f(x)=-1/x for all nonzero numbers x. If   [#permalink] 07 Oct 2019, 00:56
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