EDB — 1X3

[1X3] Let $A,B\subseteq ℝ$ and let $f:A\to B$ be defined by the formula $f(x)=x^2$; tell if, for the following choices of $A,B$, the function $f$ is injective and/or surjective.

1. $A=ℝ,B=ℝ$

2. $A=ℝ,B=[0,\infty )$

3. $A=[0,\infty ),B=ℝ$

4. $A=[0,\infty ),B=[0,\infty )$

If the function is bijective, what is its inverse commonly called?

(This exercise is to make you ponder about the difference between ”formula” and ”function.”