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Determine the range of the function f(x) = sin⁻¹x + tan⁻¹x + sec⁻¹x.

1. (π/4, 3π/4)
2. [π/4, 3π/4]
3. {π/4, 3π/4}
4. None of these

Correct answer: {π/4, 3π/4}

Solution

sin^-1 needs |x|<=1 and sec^-1 needs |x|>=1, so the domain is just x=+-1. At x=1: pi/2+pi/4+0 = 3pi/4. At x=-1: -pi/2-pi/4+pi = pi/4. Range = {pi/4, 3pi/4}.

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