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

Chanel Hunter

Chanel Hunter

Answered question

2023-02-27

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

Answer & Explanation

Caiden Mitchell

Caiden Mitchell

Beginner2023-02-28Added 3 answers

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.

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