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# If f(x) = x/(x + 1), what is f(1/x) in terms of x ?

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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  12 Nov 2007, 13:44
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Question Stats:

49% (02:05) correct 51% (00:51) wrong based on 110 sessions
If $$f(x) = \frac{x}{x + 1}$$, what is $$f(\frac{1}{x})$$ in terms of $$f(x)$$?

A. $$f(x)$$
B. $$-f(x)$$
C. $$\frac{1}{f(x)}$$
D. $$1 - f(x)$$
E. none of the above

M19-14
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Sep 2014, 22:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  12 Nov 2007, 13:48
bmwhype2 wrote:
F(x) = x/(x+1).
What is f(1/x) in terms of f(x)?

f(x)
-f(x)
1/f(x)
1-F(x)
none of the above

can someone give me a step by step breakdown? I got stuck after 1/(1+x)

f(1/x) = (1/x)/((1/x)+1)==> 1/(1+x)

trying chice D 1-Fx

1- x/(1+x)=== > x+1-x/(1+x)===> 1/(1+x)

so we can see f(1/x)= 1/(1+x) == 1-f(x)

Answe D
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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  12 Nov 2007, 19:52
1
KUDOS
after you have broken down to (1/1+x)

test a number, say x=2...

f(2)=2/3

f(1/2)=1/3

which is same as 1-f(x)...

D it is..
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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  12 Nov 2007, 20:31
fresinha12 wrote:
after you have broken down to (1/1+x)

test a number, say x=2...

f(2)=2/3

f(1/2)=1/3

which is same as 1-f(x)...

D it is..

Solved it the same way to get D.
CEO
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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  15 Nov 2007, 02:16
fresinha12 wrote:
after you have broken down to (1/1+x)

test a number, say x=2...

f(2)=2/3

f(1/2)=1/3

which is same as 1-f(x)...

D it is..

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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  25 Sep 2014, 20:39
$$f(x) = \frac{x}{x+1}$$

$$f(\frac{1}{x}) = \frac{\frac{1}{x}}{\frac{1}{x} + 1} = \frac{1}{x+1}$$

$$1 - f(x) = 1 - \frac{x}{x+1} = \frac{1}{x+1}$$

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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ? [#permalink]  25 Sep 2014, 22:31
Expert's post
bmwhype2 wrote:
If $$f(x) = \frac{x}{x + 1}$$, what is $$f(\frac{1}{x})$$ in terms of $$f(x)$$?

A. $$f(x)$$
B. $$-f(x)$$
C. $$\frac{1}{f(x)}$$
D. $$1 - f(x)$$
E. none of the above

M19-14

$$f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} = \frac{1}{1 + x} = \frac{1 + x - x}{1 + x} = 1 - \frac{x}{1 + x} = 1 - f(x)$$.

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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?   [#permalink] 25 Sep 2014, 22:31
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