Question:

<div class="solution"><p>x-sin x is odd increasing. For x>0: f'(x)=(x-sin x)+x(1-cos x)>0 \to strictly increasing. Odd, range=ℝ \to bijective.</p><p><strong>Answer: (C) bijective</strong></p><div class="trap-box"><strong>Trap:</strong> The |x| factor preserves oddness since it multiplies another odd factor.<div class="key-concept"><strong>Key Concept:</strong> Odd \times odd = even? No -- |x| is even, (x-sin x) is odd, product is odd