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# If f(x) = (x+1)/(x-1), then the ratio of x to f(y)

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Joined: 28 May 2014
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GMAT 1: 730 Q49 V41
If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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24 Feb 2017, 03:05
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If f(x) = (x+1)/(x-1), then the ratio of x to f(y) where y = f(x) is:

(A) x : y
(B) x^2 : y^2
(C) 1 : 1
(D) y : x
(E) x^2 : y

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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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24 Feb 2017, 03:18
C
1:1 is the correct answer, if you expand y = f(x) it results in y=x.
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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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24 Feb 2017, 21:38
replace x in f(x)=(x+1)/ (x-1) with (x+1)/(x-1) and solving -> f(y)= x

x/f(y)=1
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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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24 Feb 2017, 23:22
1
I get putting in f(x) for x in to the equation for f(y). This results in:

f(y) = [((x + 1) / (x-1)) + 1] / [((x+1) / (x-1))-1]

can someone illustrate the simplification steps to get to f(y) = x ? It's not apparent to me from these explanations.
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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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25 Feb 2017, 00:16
1
jjamieson42 wrote:
I get putting in f(x) for x in to the equation for f(y). This results in:

f(y) = [((x + 1) / (x-1)) + 1] / [((x+1) / (x-1))-1]

can someone illustrate the simplification steps to get to f(y) = x ? It's not apparent to me from these explanations.

Hi jjamieson42

Let me try to explain.
Given $$f(x) = \frac{x+1}{x-1}, x \neq 1$$ and $$y = f(x)$$

$$f(y) =\frac{ \frac{x+1}{x-1} + 1}{\frac{x+1}{x-1} - 1} = \frac{\frac{x + 1 + x - 1}{x-1}}{\frac{x+1 - x + 1}{x-1}} = \frac{2x}{2} = x$$

Hope it helps.

We can solve this question by plug in the value.
Take x =2 , $$y = f(x) = \frac{2+1}{2-1} = 3$$

$$f(y) = f(3) = \frac{3+1}{3-1} = 2 = x$$ => x=f(y) => x:f(y) = 1:1 . Answer (C).

Thanks.
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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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27 Feb 2017, 12:00
saswata4s wrote:
If f(x) = (x+1)/(x-1), then the ratio of x to f(y) where y = f(x) is:

(A) x : y
(B) x^2 : y^2
(C) 1 : 1
(D) y : x
(E) x^2 : y

We can let x = 2; thus f(2) = (2 + 1)/(2 - 1) = 3/1 = 3.

Since y = f(2), y = 3.

Thus f(y) = f(3) = (3 + 1)/(3 - 1) = 4/2 = 2.

So, the ratio of x to f(y) is 2 : 2, or 1 : 1.

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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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27 Oct 2018, 11:45
Simply solve

f(y)=x+1x−1+1x+1x−1−1=x+1+x−1x−1x+1−x+1x−1=2x2=x

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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)  [#permalink]

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27 Oct 2018, 12:27
need to find x/ f(f(x))

on solving f(y)= (y+1)/(y-1)
replacing y with f(x)
[(x+1/x-1)+1]/[(x+1/x-1)-1] = x

so x/x -
1/1 = (C)
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Re: If f(x) = (x+1)/(x-1), then the ratio of x to f(y)   [#permalink] 27 Oct 2018, 12:27
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