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Find the range of fog(x) = f(g(x)) = f(4x(1 − x)).

1. [0, 1]
2. [0, 2]
3. [1, 2]
4. [−1, 1]

Correct answer: [0, 1]

Solution

The function g(x) = 4x(1 − x) has a range of [0, 1] since it represents a quadratic function with a maximum value of 1. Applying f to this range preserves [0, 1].

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