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A function f(x) is defined only on the interval [0, 1]. Find the domain of (i) f(sin x) and (ii) f(2x + 3).

1. (i) union over n of [2n*pi, (2n+1)*pi]; (ii) [-3/2, -1]
2. (i) [0, pi]; (ii) [-1, -3/2]
3. (i) all real x; (ii) [-3/2, 1]
4. (i) [0, pi/2]; (ii) [0, 1]

Correct answer: (i) union over n of [2n*pi, (2n+1)*pi]; (ii) [-3/2, -1]

Solution

f accepts inputs only in [0, 1], so set its argument between 0 and 1 and solve for x.

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