Question

If $f : \mathbb{R} \to \mathbb{R}$ is a function defined by $f(x) = x^2$, 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 neither 1-1 nor onto
• D. $f$ is both 1-1 and onto
• E. $f^{-1} : \mathbb{R} \to \mathbb{R}$ exists

Hint:

Quadratic functions over $\mathbb{R}$ are never one-to-one unless domain is restricted.

Answer 1

The Correct Option is C