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$Let f : R \to R and f_{n} (x) = f (f_{n - 1} (x)) \forall n \geq 2, n \in N$ $the roots of equation f_{3} (x) f_{2} (x) f (x) - 25 f_{2} (x) f (x) + 175 f (x) = 375$ $w h i c h a l s o s a t i s f i e s t h e e q u t i o n f (x) = x$

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$Both (a) and (b)$

answer is D.

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Detailed Solution

$\begin{matrix} f_{2} (x) = f (f (x)) = f (x) = x \\ f_{3} (x) = x \\ it gives x^{3} - 25 x^{2} + 175 x - 375 = 0 \\ (x - 5) (x^{2} - 20 x + 75) = 0 \\ {(x - 5)}^{2} (x - 15) = 0 \end{matrix}$

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