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Let f(x) =(alphax)/(x+1) Then the value ...

Let `f(x) =(alphax)/(x+1)` Then the value of `alpha` for which `f(f(x) = x` is

Text Solution

Verified by Experts

The correct Answer is:
-1
`f(x)=(alpha x)/(x+1), x ne -1`
Now `f(f(x))=x`
`implies(alpha((alpha x)/(x+1)))/((alpha x)/(x+1)+1)=x`
`implies(alpha^(2)x)/((alpha +1)x+1)=x`
`implies (alpha+1)x^(2)+(1-alpha^(2))x=0 " ...(1)" `
Now this is true for all real x.
`implies alpha +1=0 " and " 1-alpha^(2)=0`
`implies alpha = -1 ` (common value)
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