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

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink]
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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]
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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 $$ab = \frac{-1}{\frac{1}{6}} = -6$$

$$b = \frac{-6}{2} = -3$$

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

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

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]
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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

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

Function question 12.png [ 216.81 KiB | Viewed 36568 times ]

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink]
$$f(x)= -\frac{1}{x}$$

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

a = 2

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

ab = -6

2b = -6
b = -3

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Re: The function f is defined by f(x) = - 1/x for all nonzero numbers x. [#permalink]
Top Contributor
$$f(x)= -\frac{1}{x}$$

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

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