Let , . Then, for what value of is ?
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: D
Solution
f(f(x)) = f(αx/(x+1)) = α·(αx/(x+1)) / (αx/(x+1) + 1) = α²x / (αx + x + 1).
For f(f(x)) = x, we need α²x = x(αx + x + 1), i.e., α² = αx + x + 1 for all x. The coefficient of x must be zero: α + 1 = 0, giving α = -1, and then α² = 1 ✓.
For f(f(x)) = x, we need α²x = x(αx + x + 1), i.e., α² = αx + x + 1 for all x. The coefficient of x must be zero: α + 1 = 0, giving α = -1, and then α² = 1 ✓.
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