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# If f(x)=1-(1/x), then f(f(f(x)))=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82
If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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28 Dec 2018, 03:21
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:53) correct 30% (02:22) wrong based on 43 sessions

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[Math Revolution GMAT math practice question]

If $$f(x)=1-(\frac{1}{x})$$, then $$f(f(f(x)))$$=?

$$A. x$$
$$B. \frac{1}{x}$$
$$C. \frac{1}{x+1}$$
$$D. \frac{-1}{x+1}$$
$$E. \frac{x}{x+1}$$

_________________
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 $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" VP Joined: 09 Mar 2018 Posts: 1004 Location: India Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 28 Dec 2018, 04:16 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$f(x)=1-(\frac{1}{x})$$, then $$f(f(f(x)))$$=? $$A. x$$ $$B. \frac{1}{x}$$ $$C. \frac{1}{x+1}$$ $$D. \frac{-1}{x+1}$$ $$E. \frac{x}{x+1}$$ Inline are my 2 cents We will solve this question step by step $$f(x)=1-(\frac{1}{x})$$, then $$f(f(f(x)))$$ = ? Step 1 => f(x)= (x-1) / x substitute in f(f((x-1)/x)) Solving which will give f(-1/(x-1)) -------------(1) Step 2 => Now substitute (1) in $$f(x)=1-(\frac{1}{x})$$ as value of x Solving which will give =>$$\frac{-1 - x + 1}{x-1}$$ *$$\frac{x-1}{-1}$$ Giving answer as x Correct Answer A _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. CEO Joined: 18 Aug 2017 Posts: 3879 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 28 Dec 2018, 04:55 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$f(x)=1-(\frac{1}{x})$$, then $$f(f(f(x)))$$=? $$A. x$$ $$B. \frac{1}{x}$$ $$C. \frac{1}{x+1}$$ $$D. \frac{-1}{x+1}$$ $$E. \frac{x}{x+1}$$ given $$f(x)=1-(\frac{1}{x})$$ so substitute value of F(x) in $$f(f(f(x)))$$ we would get -1/x-1 again for f(x) substitute -1/x-1 we would get 1- 1/ ( -1/x-1) solving which we would get ; +x IMO A _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. GMAT Tutor Joined: 07 Nov 2016 Posts: 56 GMAT 1: 760 Q51 V42 Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 28 Dec 2018, 07:45 1 f(x) = 1 - (1/x) Let x = 2 f(2) = 1 - (1/2) = (1/2) = 0.5 f(f(2)) = 1 - (1/0.5) = - 1 f(f(f(2))) = 1 - 1/(-1) = 2 = x To be sure we can check by substituting x = 2 in the other choices Only Choice A matches Choice A _________________ Please contact me at ksrutisagar@gmail.com VP Joined: 09 Mar 2018 Posts: 1004 Location: India Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 28 Dec 2018, 08:19 ksrutisagar Would you recommend plugging in a value, a good strategy for such questions ?? Thank you for sharing your thoughts. _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. GMAT Tutor Joined: 07 Nov 2016 Posts: 56 GMAT 1: 760 Q51 V42 Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 28 Dec 2018, 08:48 1 KanishkM wrote: ksrutisagar Would you recommend plugging in a value, a good strategy for such questions ?? Thank you for sharing your thoughts. Yes, as it is much simpler and more accurate to work with numbers than variables However you have to be careful while plugging in values. For example x = 1 would not work as denominator would become zero in the second step _________________ Please contact me at ksrutisagar@gmail.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7465 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If f(x)=1-(1/x), then f(f(f(x)))=? [#permalink] ### Show Tags 30 Dec 2018, 18:32 => $$f(x) = 1 – \frac{1}{x} = \frac{(x-1)}{x}$$ $$f(f(x)) = 1 – \frac{1}{f(x)} = 1 – \frac{x}{(x-1)} = \frac{(x-1-x)}{(x-1)} = \frac{- 1}{(x-1)}$$ $$f(f(f(x))) = 1 – \frac{1}{f(f(x))} = 1 – ( - (x-1)) = 1 + x – 1 = x$$ 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$149 for 3 month Online Course"
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?   [#permalink] 30 Dec 2018, 18:32
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# If f(x)=1-(1/x), then f(f(f(x)))=?

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