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Let f: R -> R be defined by f(x) = 7x³ + 6x² + 12x + 3*cos x - 4*sin x. Then f is

1. Injective
2. Surjective
3. Bijective
4. Not Surjective

Correct answer: Bijective

Solution

If the derivative is positive everywhere, f is strictly increasing, hence injective; being an unbounded continuous function it also covers all of R, hence surjective, so it is bijective.

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