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5 replies to this topic

#1 BMAD

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Posted 20 May 2013 - 07:04 PM

Many of my algebra and precalculus students think the 'inverse function' of f(x), often written f^(-1)(x), is the same as the reciprocal 1/f(x) (mistaking the -1 for an exponent).  This (as I am obliged to remind them) is almost always false. But can you find at least one function whose inverse is also its reciprocal? Tiebreaker: Find as many as you can!

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#2 kingofpain

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Posted 22 May 2013 - 06:25 PM

Spoiler for hmmm...


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#3 bonanova

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Posted 23 May 2013 - 11:56 AM

There are a few functions that are their own inverses. 1/x (away from 0) is one instance.
For tiebreaker are you asking for other instances of functions for which f[f(x)]= x?
Or for more functions whose inverses are their reciprocals?
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Vidi vici veni.


#4 BMAD

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Posted 23 May 2013 - 12:36 PM

There are a few functions that are their own inverses. 1/x (away from 0) is one instance.
For tiebreaker are you asking for other instances of functions for which f[f(x)]= x?
Or for more functions whose inverses are their reciprocals?


The latter
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#5 kingofpain

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Posted 23 May 2013 - 06:57 PM

Spoiler for unbroken ties...


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#6 James33

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Posted 23 May 2013 - 07:19 PM

 

Spoiler for unbroken ties...

 

 

I think the OP means that f^-1(x)=1/f(x).

 

Spoiler for


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