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For the function f(x)=√(x-√(1-x²)), what is its domain?

1. [-1,-1/√(2)]∪[1/√(2),1]
2. [-1,1]
3. (-∞,-1/2]∪[1/√(2),+∞)
4. [1/√(2),1]

Correct answer: [1/√(2),1]

Solution

Require 1-x^2 >= 0 so x in [-1,1], and x - sqrt(1-x^2) >= 0 means x >= sqrt(1-x^2), which forces x >= 0 and x^2 >= 1-x^2, i.e. x >= 1/sqrt(2). Combining gives the domain [1/sqrt(2), 1].

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