Answer to Question #308080 in Calculus for Fellix

Question

Question 4 [7]

Prove that 𝑓(𝑥) = 𝑥^2 + 2𝑥 is not injective.

Answer 1

Since $𝑓(0) = 0^2 + 2\cdot 0=0$ and $𝑓(-2) = (-2)^2 + 2(-2)=4-4=0,$we conclude that $f(0)=f(-2),$ and hence $f$ is not injective.