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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 ## If f(x)=1-(1/x), then f(f(f(x)))=? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 1 member reply ### GMAT/MBA Expert ## If f(x)=1-(1/x), then f(f(f(x)))=? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] If f(x)=1-(1/x), then f(f(f(x)))=? A. x B. 1/x C. 1/x+1 D. -1/x+1 E. x/x+1 _________________ 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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Junior | Next Rank: 30 Posts
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f(x) = 1-(1/x)
f(x) = (x-1)/x

f(f(x)) implies substituting f(x) as x in above expression
f(f(x)) = (1-(1/x) -1 )/(1-(1/x))
f(f(x)) = -1/(x-1)

f(f(f(x))) = f(-1/(x-1))
Substituting 'x' as -1/(x-1) in f(x)
f(f(f(x))) = 1 - (1/(-1/(x-1)))
f(f(f(x))) = 1 + x -1
f(f(f(x))) = x
So, Option A is correct

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

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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 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Max@Math Revolution wrote: [Math Revolution GMAT math practice question] If f(x)=1-(1/x), then f(f(f(x)))=? A. x B. 1/x C. 1/x+1 D. -1/(x+1) E. x/(x+1) Let x=2 and apply the function three times: f(2) = 1 - 1/2 = 1/2. f(1/2) = 1 - 1/(1/2) = -1. f(-1) = 1 - (1/-1) = 2. The correct answer must yield a value of 2 when x=2. Only A works. The correct answer is A. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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