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Consider the functions f(x) = max {1 + sin(x), 1 - cos(x)} for x in the interval [0, 2π], and g(x) = max {1, |x - 1|} for x belonging to the set of real numbers. Which of the following is true?

1. The value of g(f(0)) is equal to 1.
2. The value of g(f(0)) is equal to 1.
3. The value of f(g(1)) is equal to 1.
4. The value of f(g(0)) is equal to 1 + sin(1).

Correct answer: The value of g(f(0)) is equal to 1.

Solution

The value of g(f(0)) is equal to 1 because f(0) = max {1 + sin(0), 1 - cos(0)} = max {1, 0} = 1, and g(1) = max {1, |1 - 1|} = max {1, 0} = 1.

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