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

So y = x − 2 x + 1 = ( x − 1 ) 2 x = ( 1 ± y ) 2 = 1 ± 2 y + yso f − 1 ( x ) = x ± 2 x + 1Specifically f − 1 ( x ) = x + 2 x + 1 when x ≥ 1 and f − 1 ( x ) = x − 2 x + 1 when 0 ≤ x ≤ 1.

Expert answers to "Find the inverse function of f ( x..."

Frank Day

Answered question

2022-07-09

Find the inverse function of

f (x) = x - (2 \sqrt{x}) + 1

the domain of definition is

x \geq 0

Answer & Explanation

Gornil2

Beginner2022-07-10Added 20 answers

y = x - 2 \sqrt{x} + 1 = (\sqrt{x} - 1)^{2}

x = (1 \pm \sqrt{y})^{2} = 1 \pm 2 \sqrt{y} + y

f^{- 1} (x) = x \pm 2 \sqrt{x} + 1

Specifically

f^{- 1} (x) = x + 2 \sqrt{x} + 1

when

x \geq 1

and

f^{- 1} (x) = x - 2 \sqrt{x} + 1

when

0 \leq x \leq 1

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