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

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If a function f is defined by f(x)= -1/x for all non zero numbers x. I [#permalink]  16 Dec 2010, 17:37
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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
[Reveal] Spoiler: OA

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Re: If a function f is defined by f(x)= -1/x for all non zero numbers x. I [#permalink]  16 Dec 2010, 18:34
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 nu [#permalink]  14 Feb 2011, 16:52
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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 $$ab=-6$$ --> $$2b=-6$$ --> $$b=-3$$.

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Re: The function f is defined by f(x) = - 1/x for all nonzero nu [#permalink]  29 Oct 2014, 23:44
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 $$ab = \frac{-1}{\frac{1}{6}} = -6$$

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

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Re: If a function f is defined by f(x)= -1/x for all non zero numbers x. I [#permalink]  30 Jan 2015, 03:55
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Re: If a function f is defined by f(x)= -1/x for all non zero numbers x. I   [#permalink] 30 Jan 2015, 03:55
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