Question

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x|x+2| \) is:

• A. one one but not onto
• B. onto but not one one
• C. both one one and onto
• D. neither one one nor onto

Hint:

To quickly check if a continuous function is onto \( \mathbb{R} \), check its limits at \( \pm \infty \). To check if it's one-one, look for symmetry or roots; here, \( x=0 \) and \( x=-2 \) both being roots immediately proves it is many-to-one.

Answer 1

The Correct Option is B