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$Let f (x) = \frac{α x}{(x + 1)}, x \neq - 1 . Then for what value of α is f (f (x)) = x ?$

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detailed solution

Correct option is D

f(x)=αxx+1,x≠−1 f(f(x))=x or α∞xx+1αxx+1+1=x or α2x(α+1)x+1=x or (α+1)x2+1−α2x=0 or α+1=0 and 1−α2=0 [As it is true ∀x≠−1 , Eq. (1) is an identity] or α=−1

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Let f(x)=αx(x+1),x≠−1. Then for what value of α is f(f(x))=x?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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$Let f (x) = \frac{α x}{(x + 1)}, x \neq - 1 . Then for what value of α is f (f (x)) = x ?$