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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## f(2x-1) = ( x + 2 ) / ( x - 2 ). What is f(x)? tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 0 member replies ### GMAT/MBA Expert ## f(2x-1) = ( x + 2 ) / ( x - 2 ). What is f(x)? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] f(2x-1) = ( x + 2 ) / ( x - 2 ). What is f(x)? A. f(x) = ( x + 5 ) / ( x - 3 ) B. f(x) = ( x - 5 ) / ( x + 3 ) C. f(x) = ( x + 5 ) / ( x + 3 ) D. f(x) = ( x - 5 ) / ( x - 3 ) E. f(x) = ( x + 3 ) / ( x - 3 ) _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

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

A. f(x) = ( x + 5 ) / ( x - 3 )
B. f(x) = ( x - 5 ) / ( x + 3 )
C. f(x) = ( x + 5 ) / ( x + 3 )
D. f(x) = ( x - 5 ) / ( x - 3 )
E. f(x) = ( x + 3 ) / ( x - 3 )
Let x=1.
Plugging x=1 into f(2x-1) = ( x + 2 ) / ( x - 2 ), we get:
f(2*1 - 1) = (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) = (1+5)/(1-3) = 6/-2 = -3.

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Max@Math Revolution wrote:
[GMAT math practice question]

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

A. f(x) = ( x + 5 ) / ( x - 3 )
B. f(x) = ( x - 5 ) / ( x + 3 )
C. f(x) = ( x + 5 ) / ( x + 3 )
D. f(x) = ( x - 5 ) / ( x - 3 )
E. f(x) = ( 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.

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We solve this problem using a change of variable. Let t = 2x -1.
Then 2x = t + 1 or x = ( 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)
= ( t + 5 ) / ( t - 3 ).
Making the substitution t = x gives
f(x) = ( x + 5 ) / ( x - 3 ).

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution wrote: [GMAT math practice question] f(2x-1) = ( x + 2 ) / ( x - 2 ). What is f(x)? A. f(x) = ( x + 5 ) / ( x - 3 ) B. f(x) = ( x - 5 ) / ( x + 3 ) C. f(x) = ( x + 5 ) / ( x + 3 ) D. f(x) = ( x - 5 ) / ( x - 3 ) E. f(x) = ( 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, letâ€™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, letâ€™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. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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