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# f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

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31 Jan 2019, 02:16
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55% (hard)

Question Stats:

55% (02:07) correct 45% (02:25) wrong based on 38 sessions

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[GMAT math practice question]

$$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$. What is $$f(x)$$?

$$A. f(x) = \frac{( x + 5 )}{( x – 3 )}$$
$$B. f(x) = \frac{( x - 5 )}{( x + 3 )}$$
$$C. f(x) = \frac{( x + 5 )}{( x + 3 )}$$
$$D. f(x) = \frac{( x – 5 )}{( x – 3 )}$$
$$E. f(x) = \frac{( x + 3 )}{( x – 3 )}$$

_________________
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1028 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? [#permalink] ### Show Tags 31 Jan 2019, 03:04 f(2x-1) = f(x) Now we have to replace 2x-1 by x, i.e, 2x-1 = x then x = 1 f(2x-1) = -3 Now put x = 1 in all the options, Only Option A yields -3. A is the answer. _________________ Press +1 Kudos If my post helps! GMAT Club Legend Joined: 18 Aug 2017 Posts: 4976 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? [#permalink] ### Show Tags 31 Jan 2019, 03:06 1 MathRevolution wrote: [GMAT math practice question] $$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$. What is $$f(x)$$? $$A. f(x) = \frac{( x + 5 )}{( x – 3 )}$$ $$B. f(x) = \frac{( x - 5 )}{( x + 3 )}$$ $$C. f(x) = \frac{( x + 5 )}{( x + 3 )}$$ $$D. f(x) = \frac{( x – 5 )}{( x – 3 )}$$ $$E. f(x) = \frac{( x + 3 )}{( x – 3 )}$$ from given answer options do plugin of f(x) as f(2x-1) in option A we get $$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$ IMO A _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? [#permalink] ### Show Tags 31 Jan 2019, 04:21 MathRevolution wrote: [GMAT math practice question] $$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$. What is $$f(x)$$? $$A. f(x) = \frac{( x + 5 )}{( x – 3 )}$$ $$B. f(x) = \frac{( x - 5 )}{( x + 3 )}$$ $$C. f(x) = \frac{( x + 5 )}{( x + 3 )}$$ $$D. f(x) = \frac{( x – 5 )}{( x – 3 )}$$ $$E. f(x) = \frac{( x + 3 )}{( x – 3 )}$$ Let x=1. Plugging x=1 into $$f(2x-1) = \frac{x + 2}{x – 2}$$, we get: $$f(2*1-1) = \frac{1 + 2}{1 – 2}$$ $$f(1) = -3$$ When x=1, the question stem becomes: What is $$f(1)$$? Since f(1) = -3, the correct answer must yield -3 when x=1. Only A works: $$f(1) = \frac{1 + 5}{1-3}$$ = -3 _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? [#permalink] ### Show Tags 31 Jan 2019, 05:39 MathRevolution wrote: [GMAT math practice question] $$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$. What is $$f(x)$$? $$A. f(x) = \frac{( x + 5 )}{( x – 3 )}$$ $$B. f(x) = \frac{( x - 5 )}{( x + 3 )}$$ $$C. f(x) = \frac{( x + 5 )}{( x + 3 )}$$ $$D. f(x) = \frac{( x – 5 )}{( x – 3 )}$$ $$E. f(x) = \frac{( x + 3 )}{( x – 3 )}$$ $$? = f\left( x \right)$$ $$f\left( {2x - 1} \right) = {{x + 2} \over {x - 2}}\,\,\,\,\,\left( * \right)$$ $$2x - 1 = y\,\,\,\,\, \Rightarrow \,\,\,\,x = {{y + 1} \over 2}$$ $$\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,f\left( y \right)\,\, = \,\,{{{{y + 1} \over 2} + 2} \over {{{y + 1} \over 2} - 2}}\,\, = \,\,{{y + 1 + 4} \over {y + 1 - 4}} = {{y + 5} \over {y - 3}}$$ $$?\,\,\,:\,\,\,f\left( y \right) = {{y + 5} \over {y - 3}}\,\,\,\,\,\,\,\left[ {\,f\left( x \right) = {{x + 5} \over {x - 3}}\,\,\,{\rm{if}}\,\,{\rm{you}}\,\,{\rm{prefer}}!\,} \right]$$ The correct answer is therefore (A). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7999 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? [#permalink] ### Show Tags 04 Feb 2019, 05:40 => We solve this problem using a change of variable. Let $$t = 2x -1.$$ Then $$2x = t + 1$$ or $$x = \frac{( t + 1 )}{2.}$$ $$f(2x-1) = f(t) = ( (t+1)/2 + 2 ) / ( (t+1)/2 – 2 ) = ( t + 1 + 4 ) / ( t + 1 – 4 )$$(after multiplying both top and bottom by 2) $$= \frac{( t + 5 )}{( t – 3 ).}$$ Making the substitution $$t = x$$ gives $$f(x) = \frac{( x + 5 )}{( x – 3 )}.$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?  [#permalink]

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06 Feb 2019, 19:34
MathRevolution wrote:
[GMAT math practice question]

$$f(2x-1) = \frac{( x + 2 )}{( x – 2 )}$$. What is $$f(x)$$?

$$A. f(x) = \frac{( x + 5 )}{( x – 3 )}$$
$$B. f(x) = \frac{( x - 5 )}{( x + 3 )}$$
$$C. f(x) = \frac{( x + 5 )}{( x + 3 )}$$
$$D. f(x) = \frac{( x – 5 )}{( x – 3 )}$$
$$E. f(x) = \frac{( x + 3 )}{( x – 3 )}$$

Let y = 2x - 1, so x = (y + 1)/2. In other words,

f(y) = [(y + 1)/2 + 2] / [(y + 1)/2 - 2]

f(y) = (y + 1 + 4) / (y + 1 - 4)

f(y) = (y + 5) / (y - 3)

Now we can replace y with x and obtain:

f(x) = (x + 5) / (x - 3)

Alternate Solution:

First, let’s take x = -2 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(-2) - 1) = (-2 + 2) / (-2 - 2)

f( -5) = 0

Looking at the answer choices, we observe that only A and C equal zero when x = -5; therefore we eliminate B, D and E.

Next, let’s take x = 3 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(3) - 1) = (3 + 2) / (3 - 2)

f(5) = 5

In answer choice C, when we take x = 5, we obtain f(5) = 10/8, which is not equal to 5. Therefore, we eliminate C as well. The only remaining answer choice is A. Indeed, for the function in A, if we take x = 5, we obtain f(5) = (5 + 5) / (5 - 3) = 10/2 = 5.

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Re: f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?   [#permalink] 06 Feb 2019, 19:34
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