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Manager
Joined: 27 May 2010
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If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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17 Jun 2019, 22:45
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If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x) such that f2(J(f1(x))) = f3(x) A) f1(x) B) f3(x)/x C) f3(x) D) f2(x) E) f2(x)/x
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Senior Manager
Joined: 09 Jun 2014
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jun 2019, 08:22
prashanths wrote: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x) such that f2(J(f1(x))) = f3(x)
A) f1(x) B) f3(x)/x C) f3(x) D) f2(x) E) f2(x)/x Can someone please help me with approach of this problem. I guess it involves F inverse.



Manager
Joined: 21 Feb 2019
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jun 2019, 08:49
\(f_2 (J(f_1)) = f_3\) \(1  J(\frac{1}{x}) = \frac{1}{1x}\) \(J(\frac{1}{x}) =  \frac{x}{1x}\) To get \(J(x)\), you need to reverse \(x\) to the power of negative 1. So you derive \(J(x) = \frac{1}{1 x}\). Correct answer is C.
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Senior Manager
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jun 2019, 09:09
lucajava wrote: \(f_2 (J(f_1)) = f_3\)
\(1  J(\frac{1}{x}) = \frac{1}{1x}\)
\(J(\frac{1}{x}) =  \frac{x}{1x}\)
To get \(J(x)\), you need to reverse \(x\) to the power of negative 1. So you derive \(J(x) = \frac{1}{1 x}\). Correct answer is C. Thanks Lucajava. I was missing this highligted text.



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Joined: 19 Oct 2018
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If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jun 2019, 11:23
\(f_2(J(f_1(x)))= f_3(x)\) \(1J(\frac{1}{x})\)=\(\frac{1}{(1x)}\) \(J(\frac{1}{x})\)=\(\frac{x}{(1x)}\) \(J(\frac{1}{x})\)= (1/x)/[1(1/x)] \(J(x)=\frac{x}{(1x)}\) prabsahi wrote: prashanths wrote: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x) such that f2(J(f1(x))) = f3(x)
A) f1(x) B) f3(x)/x C) f3(x) D) f2(x) E) f2(x)/x Can someone please help me with approach of this problem. I guess it involves F inverse.



Manager
Joined: 11 Feb 2018
Posts: 74

Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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22 Jun 2019, 08:09
lucajava wrote: \(f_2 (J(f_1)) = f_3\)
\(1  J(\frac{1}{x}) = \frac{1}{1x}\)
\(J(\frac{1}{x}) =  \frac{x}{1x}\)
To get \(J(x)\), you need to reverse \(x\) to the power of negative 1. So you derive \(J(x) = \frac{1}{1 x}\). Correct answer is C. Hi could you please elaborate on the solution. Unfortunately I am not following. I got the right answer by substitution functions one at a time but took 4+ minutes.



Manager
Joined: 21 Feb 2019
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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23 Jun 2019, 08:25
aliakberza wrote: lucajava wrote: \(f_2 (J(f_1)) = f_3\)
\(1  J(\frac{1}{x}) = \frac{1}{1x}\)
\(J(\frac{1}{x}) =  \frac{x}{1x}\)
To get \(J(x)\), you need to reverse \(x\) to the power of negative 1. So you derive \(J(x) = \frac{1}{1 x}\). Correct answer is C. Hi, could you please elaborate on the solution. Unfortunately, I am not following it. I got the right answer by substitution functions one at a time but took 4+ minutes. So, we are demanded to find out what is \(J(x)\) such that \(f_2 (J(f_1(x))) = f_3(x)\). We know that \(f_2(x) = 1  x\). Thus, \(f_2(J(f_1(x)) = 1  J(f_1(x)\). Now, knowing that \(f_1(x) = \frac{1}{x}\), we can rewrite it as \(f_2(J(f_1(x)) = 1  J(\frac{1}{x})\). Turn back to the original equation, and substitute what we've found into it: \(1  J(\frac{1}{x}) = \frac{1}{1x}\). After some computations, we derive \(J(\frac{1}{x}) =  \frac{x}{1x}\). To get \(J(x)\), you need to raise \(x\) to the 1 power. In fact \(\frac{1}{x}^{1} = x\). Elaborating on this, what you find out is: \( \frac{x^{1}}{1  x^{1}} = \frac{1}{x} * \frac{x}{x  1} = \frac{1}{1  x}\). I hope it's clear!
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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23 Jun 2019, 23:34
If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x) such that f2(J(f1(x))) = f3(x) f2(J(f1(x))) = f3(x) Since f2(x) = 1  x and f3(x) = 1/(1x) f2(J(f1(x))) = 1  J(f1(x)) = 1/(1x) Since f1(x) = 1/x, J(1/x) = 1  1/(1x) = x/(1x) Substitute 1/x as x, J(x) =  (1/x)/(1  1/x) = (1/x)/((x1)/x) = 1/(1x) which equals f3(x). Option C
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Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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24 Jun 2019, 03:08
when you simplify LHS you get f2(j(1/x))=1j(1/x) 1j(1/x)=1/1x 11/1x=j(1/x) j(1/x)=1/(1/x)1=1/1(1/x)=f3



Manager
Joined: 07 May 2018
Posts: 66

Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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30 Jun 2019, 10:55
lucajava wrote: \(f_2 (J(f_1)) = f_3\)
\(1  J(\frac{1}{x}) = \frac{1}{1x}\)
\(J(\frac{1}{x}) =  \frac{x}{1x}\)
To get \(J(x)\), you need to reverse \(x\) to the power of negative 1. So you derive \(J(x) = \frac{1}{1 x}\). Correct answer is C. How do you reverse x



Senior Manager
Joined: 09 Jun 2014
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Concentration: General Management, Operations

Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jul 2019, 21:20
\(f_2(J(f_1(x)))= f_3(x)\) \(1J(\frac{1}{x})\)=\(\frac{1}{(1x)}\) \(J(\frac{1}{x})\)=\(\frac{x}{(1x)}\) \(J(\frac{1}{x})\)= (1/x)/[1(1/x)] \(J(x)=\frac{x}{(1x)}\) prabsahi wrote: prashanths wrote: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x) such that f2(J(f1(x))) = f3(x)
A) f1(x) B) f3(x)/x C) f3(x) D) f2(x) E) f2(x)/x Can someone please help me with approach of this problem. I guess it involves F inverse. [/quote] Thanks Nick!!




Re: If f1(x) = 1/x, f2(x) = 1  x, f3(x) = 1/(1x) then find J(x)
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20 Jul 2019, 21:20






