SOLUTION: For which of the following functions is f(f(x)) = x, for all values of x in the domain of f? I. f(x) = x II. f(x) = -x III. f(x) = 1/x I have looked at this for hours, but

Question 915234: For which of the following functions is f(f(x)) = x, for all values of x in the domain of f?
I. f(x) = x
II. f(x) = -x
III. f(x) = 1/x
I have looked at this for hours, but I just can't make sense of it.... Please explain and show work!
Your help is TRULY appreciated.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's try them out

I.

f(x) = x

f(f(x)) = f(x) ... replace EVERY x with f(x)

f(f(x)) = x ... replace f(x) on the right side with x (works because f(x) = x)

so statement I is true.

---------------------------------------------------------------------

II.

f(x) = -x

f(f(x)) = -(f(x))

f(f(x)) = -(-x)

f(f(x)) = x

and II is also another answer.

------------------------------------------------------------------

III.

f(x) = 1/x

f(f(x)) = 1/(f(x))

f(f(x)) = 1/(1/x)

f(f(x)) = x

========================================================================

It turns out that all three functions f(x) = x, f(x) = -x and f(x) = 1/x make f(f(x)) = x true for all allowed inputs for x.

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
http://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.915027.html
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