I am struggling with this excercise:
I want to prove that the function $f: \mathbb{R} \to \mathbb{R}$, defined by $f(x)= x^3 + x^2 – 6x$, is surjective but not injective?
I personally would calculate some numbers and show that by these examples that this function cannot be injective. Is this way a correct way to prove this?
I appreciate your answer!
Best Answer
Hint: Notice that $x^3+x^2-6x=x(x-2)(x-3)$ and then $\lim\limits_{x \to \pm \infty} f(x)= \pm \infty$.