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If for all numbers P, where P 1, the function @ is defined by P@ =

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Bunuel
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If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   08 Sep 2020, 01:30
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If for all numbers \(P\), where \(P \neq 1\), the function \(@\) is defined by \(P@ = \frac{P}{P-1}\), what is the value of \((P@)@\)?


A. \(\frac {P}{P-1}\)

B. \(\frac{1}{P}\)

C. \(P\)

D. \(2 - P\)

E. \(P - 1\)


M05-05

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C
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yashikaaggarwal
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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   08 Sep 2020, 01:35
Given: P@ = P/P-1

To find: (P@)@ = ?

Solution:
=> (P@)@
=> (P/P-1)@
=> (P/P-1)/(P/P-1)-1
=> (P)/(P-1)/{P-P+1/(p-1)}
=> (P)/(P-1)/{1/(p-1)}
=> P

Answer is C

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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   08 Sep 2020, 01:58
If for all numbers P, where P≠1, the function is defined by P@=\(\frac{P}{P−1}\) what is the value of (P@)@?

Given,

P@=\(\frac{P}{P−1}\)

(P@)@=\((\frac{P}{P−1})/(\frac{P}{P−1})-1)\)=P


A. \(\frac{P}{P−1}\)

B. [\(fraction]1/P[/fraction]\)

C. P

D. 2−P

E. P−1
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Bunuel
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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   09 Sep 2020, 01:30
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Bunuel wrote:
If for all numbers \(P\), where \(P \neq 1\), the function \(@\) is defined by \(P@ = \frac{P}{P-1}\), what is the value of \((P@)@\)?


A. \(\frac {P}{P-1}\)

B. \(\frac{1}{P}\)

C. \(P\)

D. \(2 - P\)

E. \(P - 1\)


M05-05


OFFICIAL EXPLANATION



Solution 1. Pick numbers. If \(P = 2\). Then \(P@ = \frac{2}{2 - 1} = 2\). If \(P@ = P\), then \((P@)@ = P\).

Solution 2. Algebra: \(P@ = \frac{P}{(P-1)}\). Take this value and substitute it for \(P\) to find \((P@)@\)..

\(P@ = \frac{P}{(P-1)}\).

\((P@)@ = (\frac{P}{(P-1)})@=\frac{\frac{P}{(P-1)}}{\frac{P}{(P-1)} - 1}=\frac{\frac{P}{(P-1)}}{\frac{P-(P-1)}{(P-1)}}=\frac{\frac{P}{(P-1)}}{\frac{1}{(P-1)}}=\frac{P}{(P-1)}*(P-1)=P\).


Answer: C
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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   14 Feb 2021, 18:49
Hi,
As it says this function is valid for all numbers except 1, let's set P=2

(2@)=2/2-1 = 2
(2)@=2

P stays unchanged therefore answer is C
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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink] New post   14 Sep 2022, 23:16
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Re: If for all numbers P, where P 1, the function @ is defined by P@ = [#permalink]
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