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# Ridiculous Inverse

Started by BMAD, May 20 2013 07:04 PM

5 replies to this topic

### #1

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!

### #2

Posted 22 May 2013 - 06:25 PM

Spoiler for hmmm...

### #3

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

Or for more functions whose inverses are their reciprocals?

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 greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

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 whichf[f(x)]=x?

Or for more functions whose inverses are their reciprocals?

The latter

### #5

Posted 23 May 2013 - 06:57 PM

Spoiler for unbroken ties...

### #6

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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