If f(x) = (ax + b)/(cx + d) is its own inverse, then which condition must hold?
If f(x) = (ax + b)/(cx + d) is its own inverse, then which condition must hold?
- A. a + d = 0
- B. b + c = 0
- C. a + d = 0 and b = c
- D. a = d and b = c
Answer: A) a + d = 0
Explanation: For f(f(x)) = x to hold identically for a Möbius transformation, we need a + d = 0 (when ad − bc ≠ 0). This ensures f = f⁻¹.
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