If f ( x ) = x − x 1 then number of solutions of f ( f ( f ( x )) = 1 .

f ( x ) = x − x 1 , ⇒ f ( f ( x )) = x ( x 2 − 1 ) x 4 − 3 x 2 + 1 ⇒ f ( f ( f ( x ))) = 1 ⇒ f ( f ( x )) = f − 1 ( 1 ) = 2 1 + 5 → 2 values exist Or f − 1 ( 1 ) = 2 1 − 5 → 2 values exist

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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsCompositeMedium2 minQB

MathematicsMediumsingle choice

If $f (x) = x - \frac{1}{x}$ then number of solutions of $f (f (f (x)) = 1$ .

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$f (x) = x - \frac{1}{x}, \Rightarrow f (f (x)) = \frac{x ^{4} - 3 x ^{2} + 1}{x ( x ^{2} - 1 )}$ $\Rightarrow f (f (f (x))) = 1 \Rightarrow f (f (x)) = f^{- 1} (1) = \frac{1 + 5}{2} \to 2 values exist$ Or $f^{- 1} (1) = \frac{1 - 5}{2} \to 2$ values exist

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Composite

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