The function f is defined as f ( x ) = x x - 1 , how do you find f ( f ( x ) ) ?

Question

The function f is defined as             f              (        x        )              =          x              x        -        1            , how do you find             f              (                  f                      (            x            )                          )            ?

Caiden Mitchell · Accepted Answer

Given:             f              (        x        )              =          x              x        -        1            Substitute f(x) for every x            f              (                  f                      (            x            )                          )              =                            x                      x            -            1                                                (                      x                          x              -              1                                )                -        1            Multiply 1 to the numerator and denominator to create the following:                     x        -        1                    x        -        1                        f              (                  f                      (            x            )                          )              =                            x                      x            -            1                                                (                      x                          x              -              1                                )                -        1                            x        -        1                    x        -        1                        f              (                  f                      (            x            )                          )              =                  x                    x        -        x        +        1                        f              (                  f                      (            x            )                          )              =                  x            1                  f              (                  f                      (            x            )                          )              =    x  This means that             f              (        x        )              =          x              x        -        1             is its own inverse.

The function f is defined as f ( x ) = x x - 1...

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