Is this function C → C injective?

Question

Consider f $\colon$ $\mathbb C $ $\to$ $\mathbb C$ given by f (z) = $z^3$

I know that this function is a surjection, but is it injective, thus bijective?

No, see this post: Entire one-to-one functions are linear. – Dietrich Burde Jan 27 '20 at 12:15 — Dietrich Burde, Jan 27 '20 at 12:15

score 4 · Accepted Answer · answered Jan 27 '20 at 12:03

4

No, for example $f(1) = f(e^{2\pi i/3}) = f(e^{4\pi i/3}) = 1$.

[In fact, if you solve $f(z) = w$, you will get exactly three solutions for every $w\neq 0$.]

answered Jan 27 '20 at 12:03

mrf

1 Answers1