If f ( x ) = x ( x − 1 ) is a function from [ 2 1 , ∞ ) to [ − 4 1 , ∞ ) , then { x ∈ R / f − 1 ( x ) = f ( x ) } is

Question

If f ( x ) = x ( x − 1 ) is a function from [ 2 1 ​ , ∞ ) to [ − 4 1 ​ , ∞ ) , then { x ∈ R / f − 1 ( x ) = f ( x ) } is

TestHub · Accepted Answer

{ x ∈ R / f − 1 ( x ) = f ( x ) } = { x ∈ R / ff ( x ) = x } ​ f ( f ( x )) = f ( x ( x − 1 )) = [ x ( x − 1 )] [ x ( x − 1 ) − 1 ] = x ( x − 1 ) [ x 2 − x − 1 ] f ( f ( x )) = x ⇒ x ( x − 1 ) ( x 2 − x − 1 ) = x ⇒ x ( x 3 − 2 x 2 ) = 0 ⇒ x = 0 , 2 ​

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