Question

If \( f : \mathbb{R} \to \mathbb{R} \) is a function defined by \( f(x) = \sin x \), then which of the following is true?

• A. \( f \) is 1-1 but not onto
• B. \( f \) is onto but not 1-1
• C. \( f \) is both 1-1 and onto
• D. \( f \) is neither 1-1 nor onto
• E. \( f \) has finite number of zeros

Hint:

Trigonometric functions like sine are periodic, so they are never one-one over \( \mathbb{R} \), and their range is bounded.

Answer 1

The Correct Option is D