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

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

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New post 28 Dec 2018, 03:21
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Question Stats:

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[Math Revolution GMAT math practice question]

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

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

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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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.
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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
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Re: If f(x)=1-(1/x), then f(f(f(x)))=?  [#permalink]

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New post 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
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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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