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Let f(x) = |x - 2| and g(x) = f(f(x)), x ∈ [0, 4]. Then ∫_0^4 |g(x) - f(x)| dx is equal to : (1) 3/2 (2) 1 (3) 0 (4) 1/2

1. 3/2
2. 1
3. 0
4. 1/2

Correct answer: 1

Solution

The correct option is 1 because the integral of the absolute difference between g(x) and f(x) over the interval [0, 4] evaluates to 1, indicating that there is a consistent difference between the two functions across this range.

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