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If f: [1, infinity) -> [2, infinity) is defined by f(x) = x + 1/x, find f⁻¹(x).

1. (x + sqrt(x² - 4))/2
2. x/(1 + x²)
3. (x - sqrt(x² - 4))/2
4. 1 - sqrt(x² - 4)

Correct answer: (x + sqrt(x² - 4))/2

Solution

Solving for x gives two roots; the domain restriction x >= 1 selects the larger root with the plus sign.

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