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If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do

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Bunuel
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If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   21 Feb 2016, 10:17
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If f(x) = x/(1 - x) for all values of \(x \neq 1\), for what value of x does f(x) = 2/3?

A. 0
B. 2/5
C. 4/5
D. 5/2
E. 3
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Skywalker18
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   21 Feb 2016, 11:50
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f(x) = x/(1 - x)
=> 2/3 = x/(1 - x)
=> 2- 2x = 3x
=> 5x = 2
=> x = 2/5

Answer B
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BrentGMATPrepNow
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   21 Feb 2016, 12:07
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Bunuel wrote:
If f(x) = x/(1 - x) for all values of \(x \neq 1\), for what value of x does f(x) = 2/3?

A. 0
B. 2/5
C. 4/5
D. 5/2
E. 3


I'd likely use Skywalker18's approach, but another route is to TEST the answer choices.

A. f(0) = 0/(1 - 0) = 0/1 = 0 NOPE
B. f(2/5) = 2/5/(1 - 2/5) = (2/5)/(3/5) = (2/5)(5/3) = 2/3 PERFECT!!

Answer: B

Related Resources
This free video provides information that’s useful for answering this question:
- Function notation: https://www.gmatprepnow.com/module/gmat ... /video/974

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Brent
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   22 Feb 2016, 01:05
2/3 = x/1-x
2-2x = 3x
2=5x
2/5 = x

Ans: B
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chetan2u
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   22 Feb 2016, 01:45
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Bunuel wrote:
If f(x) = x/(1 - x) for all values of \(x \neq 1\), for what value of x does f(x) = 2/3?

A. 0
B. 2/5
C. 4/5
D. 5/2
E. 3



Hi,
another way--

x/(1-x)=2/3..
or (1-x)/x=3/2..

1/x-x/x=3/2..
1/x-1=3/2..

1/x=3/2 +1..
1/x=5/2 or x=2/5 B
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink] New post   04 Jan 2022, 04:36
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Re: If f(x) = x/(1 - x) for all values of x \neq 1, for what value of x do [#permalink]
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