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Given the function f: R → R defined as f(x) = |x| (x − sin x), which of the following statements about the function is accurate?

1. f is injective but not surjective.
2. f is surjective but not injective.
3. f is both injective and surjective.
4. f is neither injective nor surjective.

Correct answer: f is both injective and surjective.

Solution

The function f(x) = |x|(x − sin x) is both injective (one-to-one) and surjective (onto) because it uniquely maps every real number to a real number and covers the entire range of real numbers.

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