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The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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16 Dec 2010, 18:37
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If a function f is defined by \(f(x)= -\frac{1}{x}\) for all non zero numbers x. If \(f(a) = -\frac{1}{2}\) and \(f(ab) = \frac{1}{6}\) then b= ?

A. 3

B. 1/3

C. -1/3

D. -3

E. -12

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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14 Feb 2011, 17:52

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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16 Dec 2010, 19:34
f(a) = -1/a = -1/2 => a=2 f(ab) = -1/ab = 1/6 => ab = -6 => b = -6/a = -6/2 = -3 Hence, D.

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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30 Oct 2014, 00:44
banksy 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 \(x = \frac{-1}{f(x)}\)

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

\(f(ab) = \frac{1}{6}\); so \(ab = \frac{-1}{\frac{1}{6}} = -6\)

\(b = \frac{-6}{2} = -3\)

Answer = D

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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10 Jul 2016, 04:57

HarveyKlaus wrote:

The function f is defined by f(x) = -1/x for all non zero 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 Any help? Thanks

Given f(x) = -1/x.

f(a) = -1/2 , then a has to be - 2.

Now we are asked to b from find f(ab) = 1/6.

In order to make positive ab = 6, this results when a = -2 then b has to be - 3.

Option D is correct answer.

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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Updated on: 10 Jul 2016, 11:35

f(x) = -1/x for all non zero numbers x.If f(a) = -1/2 and f (ab) = 1/6, then b= ? We can say that a = 2 which fits into the definition of f(x) , f(2) = -1/2. Similarly, f(ab) = - 1/ (ab) = - 1/ (-6) . So ab = -6 and a = 2 . Therefore b= -3. ANS : D

Originally posted by

target760gmat on 10 Jul 2016, 05:00.

Last edited by

target760gmat on 10 Jul 2016, 11:35, edited 1 time in total.

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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10 Jul 2016, 06:42

target760gmat wrote:

f(x) = -1/x for all non zero numbers x.If f(a) = -1/2 and f (ab) = 1/6, then b= ? We can say that a = 2 which fits into the definition of f(x) , f(2) = -1/2. Similarly, f(ab) = - 1/ (ab) = - 1/ (-6) . So ab = -6 and a = 2 . Therefore b=3. ANS :D

Hey, if ab = -6 then b has to be -3 not 3 when a = 2 . Just change it as per your solution .

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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10 Aug 2016, 11:43
HarveyKlaus wrote:

The function f is defined by f(x) = -1/x for all non zero 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

Given:

f(x) = -1/x f(a) = -1/2

So, f(a) = -1/a = -1/2

This means that a = 2

f(ab) = 1/6

So, f(ab) = -1/ab = 1/6

This means that ab = -6

If a = 2, and ab = -6, we can see that b = -3

Answer:

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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Updated on: 11 Aug 2016, 11:20

HarveyKlaus wrote:

The function f is defined by f(x) = -1/x for all non zero 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

Given that f(x) = -1/2 and f(a) = -1/2, then f(a) =-1/a=-1/2 ===> a=2, then backsolve using the answer choices:

f(ab) = f(2b) = 1/6

A) 3 ===> f(2*3) = f(6) = -1/6

B) 1/3 ===> f((2*1/3) = f(2/3) = -1/(2/3) = -3/2

C) -1/3 ===> f(2*-1/3) = f(-2/3) = -1/(-2/3) = 3/2

D) -3 ===> f(2*-3) = f(-6) = -1/-6 = 1/6 WINS

E) -12 ===> f(2*-12) = f(-24) = -1/-24 = 1/24

Answer: D

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Originally posted by

duahsolo on 11 Aug 2016, 02:32.

Last edited by

duahsolo on 11 Aug 2016, 11:20, edited 1 time in total.

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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11 Aug 2016, 11:00
ajit257 wrote:

If a function f is defined by f(x)= -1/x for all non zero 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

Given,

if f(a)=\(\frac{-1}{2}\),then a=2 if f(ab)=\(\frac{1}{6}\)=\(\frac{-1}{-6}\),then ab=-6 Since a=2,so b=\(\frac{-6}{2}\)=-3

Correct Answer D
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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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18 Jul 2017, 19:49
Here is how to do the answer broken down. A good video explaining function notation is here

https://www.youtube.com/watch?v=T6-Zdr5w_bE .

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x.
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22 Sep 2018, 02:27

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