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

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ajit257
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The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink] New post   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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D
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Bunuel
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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink] New post   14 Feb 2011, 17:52
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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


Given: \(f(x)=-\frac{1}{x}\).

As \(f(a)=-\frac{1}{a}=-\frac{1}{2}\) then \(a=2\), also as \(f(ab)=-\frac{1}{ab}=\frac{1}{6}\) then \(ab=-6\) --> \(2b=-6\) --> \(b=-3\).

Answer: D.
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The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink] New post   Updated on: 07 Jul 2020, 18:25
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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: D

Originally posted by BrentGMATPrepNow on 10 Aug 2016, 11:43.
Last edited by BrentGMATPrepNow on 07 Jul 2020, 18:25, 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. [#permalink] New post   16 Dec 2010, 19:34
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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. [#permalink] New post   30 Oct 2014, 00:44
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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. [#permalink] New post   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. [#permalink] New post   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. [#permalink] New post   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. [#permalink] New post   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

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. [#permalink] New post   11 Aug 2016, 11:00
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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. [#permalink] New post   18 Jul 2017, 19:49
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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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Function question 12.png
Function question 12.png [ 216.81 KiB | Viewed 35993 times ]

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink] New post   17 Oct 2020, 15:27
\(f(x)= -\frac{1}{x}\)

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

a = 2

\(f(ab) = \frac{1}{6}\)

ab = -6

2b = -6
b = -3

Answer is D.
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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink] New post   09 Dec 2023, 02:04
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\(f(x)= -\frac{1}{x}\)

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

\(f(ab) = -\frac{1}{ab} = \frac{1}{6}\)
=> ab = -6
=> 2 * b = -6
=> b = \(\frac{-6}{2}\) = -3

So, Answer will be D
Hope it helps!

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink]
09 Dec 2023, 02:04
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