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A function f has domain [-1, 2] and range [0, 1]. Define g(x) = 1 - f(x + 1). Find the domain and range of g, respectively.

1. [-1, 1]; [-1, 0]
2. [-2, 1]; [0, 1]
3. [0, 2]; [-1, 0]
4. [1, 3]; [-1, 0]

Correct answer: [-2, 1]; [0, 1]

Solution

For g(x) = 1 - f(x+1) to be defined, x+1 must be in [-1, 2], i.e. -2 <= x <= 1, so the domain is [-2, 1]. Since f(x+1) takes values in [0, 1], 1 - f(x+1) takes values in [1-1, 1-0] = [0, 1]. So the range is [0, 1].

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