FunctionMedium
Question
Let f(x) = 
, x ≠- 1. Then, for what of α is f [ f (x)] = x ?
, x ≠- 1. Then, for what of α is f [ f (x)] = x ?Options
A.√2
B.-√2
C.1
D.-1
Solution
Given, f(x) =
f[f(x)] = f
= x (given) ......(i)
⇒ α2 x = (α + 1) x2 + x
⇒ x[α2 - (α + 1)x -1] = 0
⇒ x(α + 1)(α - 1 - x) = 0
⇒ α - 1 = 0
⇒ α = - 1
But α = 1 does not satisfy the Eq. (i).
Therefore, (d) is the answer.
f[f(x)] = f
= x (given) ......(i)⇒ α2 x = (α + 1) x2 + x
⇒ x[α2 - (α + 1)x -1] = 0
⇒ x(α + 1)(α - 1 - x) = 0
⇒ α - 1 = 0
⇒ α = - 1
But α = 1 does not satisfy the Eq. (i).
Therefore, (d) is the answer.
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