Exercise
143
[1X3] Let \(A,B⊆ ℝ\) and let \(f:A→ B\) 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.
\(A=ℝ,B=ℝ\)
\(A=ℝ,B=[0,∞)\)
\(A=[0,∞),B=ℝ\)
\(A=[0,∞),B=[0,∞)\)
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.”