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Value at x=5....

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Value at x=5....  [#permalink]

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New post 18 Oct 2018, 10:03
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (00:51) correct 42% (00:49) wrong based on 19 sessions

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Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None
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Re: Value at x=5....  [#permalink]

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New post 18 Oct 2018, 10:20
1
adilsafder wrote:
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None


f(5) = 1/6
f{f(5)} = \(\frac{1}{(1+{1/6})}\) = \(\frac{6}{7}\)
f[f{f(x)}] = \(\frac{1}{(1+{6/7})}\) = \(\frac{7}{13}\).
Checking the answer choices and reducing to lowest terms,
Answer B.
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Re: Value at x=5....  [#permalink]

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New post 18 Oct 2018, 10:24
adilsafder wrote:
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None


OA: B

\(f(x)=\frac{1}{1+x}\)

\(f(5)=\frac{1}{1+5}=\frac{1}{6}\)

\(f(\frac{1}{6})=\frac{1}{1+\frac{1}{6}}=\frac{6}{7}\)

\(f(\frac{6}{7})=\frac{1}{1+\frac{6}{7}}=\frac{7}{13}\)

\(f[f{f(x)}],\) at \(x=5\) is \(\frac{7}{13}\) or \(\frac{21}{39}\)
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Re: Value at x=5....  [#permalink]

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New post 18 Oct 2018, 10:38
1
adilsafder wrote:
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None


OA:B

f(x)\(=\frac{1}{1+x}\)
f{f(x)}\(=\frac{1}{1+\frac{1}{1+x}}=\frac{x+1}{x+1+1}=\frac{x+1}{x+2}\)
f[f{f(x)}]\(=\frac{1}{1+\frac{x+1}{x+2}}=\frac{x+2}{x+2+x+1}=\frac{x+2}{2x+3}\)

f[f{f(5)}]\(=\frac{5+2}{2*5+3}=\frac{7}{13}\)

Multiplying denominator and numerator by \(3\) , we get

f[f{f(5)}]\(=\frac{7*3}{13*3}=\frac{21}{39}\)
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Re: Value at x=5....  [#permalink]

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New post 18 Oct 2018, 11:04
1
adilsafder wrote:
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None


This type of questions are tricky one, after finding answer for
f[f{f(5)}] = 7/13


At first instant, not finding the exact answer in answer choices, one is tempted to mark choice E, i.e. None, but as answer choices are tricky, one has to convert them to simplest form to find exact answer.
i.e. choice (B) = 21/39 = 7/13

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Re: Value at x=5....  [#permalink]

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New post 18 Oct 2018, 15:59
adilsafder wrote:
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None


One has to be careful. We should always reduce the numerator & the denominator if it allows. I got the answer 7/13 and went with E
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Re: Value at x=5....   [#permalink] 18 Oct 2018, 15:59
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