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 ho

Question 915027: 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.
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
You have three choices. Your composition equation given is to compose a function with itself. Just test every choice I, II, and III, and see which one gives x as a result (when simplified).

What if you had a forth choice...
IV.
Would this composed of itself be x?

I did not expect that, but this function is also its own inverse; meaning this function composed with itself will give back the input variable.
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