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SVP  Joined: 21 Jan 2007
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Location: New York City
If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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Question Stats: 57% (01:27) correct 43% (01:21) wrong based on 586 sessions

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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

Originally posted by bmwhype2 on 12 Nov 2007, 14:44.
Last edited by Bunuel on 25 Sep 2014, 23:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Manager  Joined: 01 Sep 2006
Posts: 235
Location: Phoenix, AZ, USA
Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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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
Current Student Joined: 28 Dec 2004
Posts: 2697
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Schools: Wharton'11 HBS'12
Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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2
1
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..
Director  Joined: 09 Aug 2006
Posts: 599
Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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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.
SVP  Joined: 21 Jan 2007
Posts: 2254
Location: New York City
Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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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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Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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3
$$f(x) = \frac{x}{x+1}$$

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

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

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

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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]

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Plug in an value to test out the effect of (1/x) over (x) when fed into the function...

Say x = 3

f(3) = 3/(3+1) = 3/4
f(1/3) = (1/3)/[(1/3)+(3/3)] = 1/4

Thus f(1/x) = 1 - f(x)
Manager  B
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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Again a good video if you're having difficulty understanding function notation is here:

Attachments gmat function question.png [ 273.28 KiB | Viewed 7879 times ]

Non-Human User Joined: 09 Sep 2013
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Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?  [#permalink]

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_________________ Re: If f(x) = x/(x + 1), what is f(1/x) in terms of x ?   [#permalink] 15 Oct 2018, 07:12
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