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If f(x) = x² + 1 and g(x) = 1/(x - 1), find the composite functions (f o g)(x) and (g o f)(x).

1. (f o g)(x) = 1/(x - 1)² + 1; (g o f)(x) = 1/x²
2. (f o g)(x) = 1/x²; (g o f)(x) = 1/(x - 1)² + 1
3. (f o g)(x) = 1/(x² + 1 - 1); (g o f)(x) = (x - 1)² + 1
4. (f o g)(x) = x²; (g o f)(x) = 1/(x² - 1)

Correct answer: (f o g)(x) = 1/(x - 1)² + 1; (g o f)(x) = 1/x²

Solution

Plug g(x) into f for f o g, and plug f(x) into g for g o f, then simplify.

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