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

Algebra ->  Rational-functions -> 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      Log On


   

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(39838) About Me  (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. f%28x%29=-1%2Fx
Would this composed of itself be x?

f%28f%28x%29%29=-1%2F%28-1%2Fx%29
1%2F%281%2Fx%29=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.