If f(x) = x² − 4x + 5 and g(x) = x − 2, then (f∘g⁻¹)(x) equals:
If f(x) = x² − 4x + 5 and g(x) = x − 2, then (f∘g⁻¹)(x) equals:
- A. x² + 1
- B. x² − 1
- C. x² − 4x + 1
- D. x² + 4x + 1
Answer: A) x² + 1
Explanation: g⁻¹(x) = x + 2. f(x) = x² − 4x + 5 = (x−2)² + 1. So (f∘g⁻¹)(x) = f(x+2) = ((x+2)−2)² + 1 = x² + 1.
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