Let `f(x)=(alphax)/((x+1)),x!=-1.` The for what value of `alpha` is `f(f(x))=x ?` `sqrt(2)` (b) `-sqrt(2)` (c) `1` (d) `-1`

Explanation

We have

`f{f(x)}=x `

`⇒f((αx)/(x+1)​)=x `

`⇒((αx)/(x+1)​)/(1+((αx)/(x+1)​))=x `

`⇒(α^2x​)/(αx+x+1)=x `

`⇒(α+1)x^2+(1−α^2)x=0`

So,

`α+1=0 or 1−α^2=0`

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