Find the inverse function of f ( x ) = x − ( 2 x...

Frank Day

Frank Day

Answered

2022-07-09

Find the inverse function of
f ( x ) = x ( 2 x ) + 1
the domain of definition is x 0

Answer & Explanation

Gornil2

Gornil2

Expert

2022-07-10Added 20 answers

So y = x 2 x + 1 = ( x 1 ) 2
x = ( 1 ± y ) 2 = 1 ± 2 y + y
so f 1 ( x ) = x ± 2 x + 1
Specifically f 1 ( x ) = x + 2 x + 1 when x 1 and f 1 ( x ) = x 2 x + 1 when 0 x 1.

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