find f^(-1) and verify that (f x f^(-1))(x)=(f^(-1) x f)(x)=x f(x)= x+3/x-2

Macioccujx

Macioccujx

Answered question

2022-07-25

Find f 1 and verify that
( f x f 1 ) ( x ) = ( f 1 x f ) ( x ) = x
f ( x ) = x + 3 / x 2

Answer & Explanation

Jaylynn Huffman

Jaylynn Huffman

Beginner2022-07-26Added 14 answers

find f 1 and verify that
( f x f 1 ) ( x ) = ( f 1 x f ) ( x ) = x
f ( x ) = x + 3 x 2 y = x + 3 x 2 y ( x 2 ) = x + 3
y x 2 y = x + 3 y x x = 2 y + 3
x ( y 1 ) = 2 y + 3 x = 2 y + 3 y 1
f 1 ( x ) = 2 x + 3 x 1
( f f 1 ) ( x ) = f ( 2 x + 3 x 1 ) = 2 x + 3 x 1 + 3 2 x + 3 x 1 2 = 2 x + 3 + 3 ( x 1 ) x 1 2 x + 3 2 ( x 1 ) x 1 = 5 x 5 = x
( f 1 f ) ( x ) = f 1 ( x + 3 x 2 ) = 2 x + 3 x 2 + 3 x + 3 x 2 1 = 2 x + 6 + 3 6 x 2 x + 3 x + 2 x 2 = 5 x 5 = x

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