Theory

Theory

• A quadratic $ax^2+bx+c$ over $\mathbb{R}$ is not one-to-one on all $\mathbb{R}$ (unless domain is restricted).
• To test surjectivity, solve $g(x)=y$ and check if real solutions exist for all $y$.
• For a quadratic, this comes down to discriminant $\Delta\ge 0$.