Let S be the set of circles in the plane, and let f : S → R be defined by: f(s) = the area of s. Is f injective? Surjective? Bijective? Explain your answer. Now let T be the set of circles in the plane whose center is the origin and define g : T → R≥0 by: g(t) = the length of the circumference of t. Is g injective? Surjective? Bijective? Explain your answer. Would your answer change if the codomain of g was R? Why or why not? Next, Let E be the set of ellipses whose major and minor axes cross the origin and define h : E → R≥0 by: h(e) = the area of e. Is h injective? Surjective? Bijective? Explain your answer. Note: Points are circles with zero radius.

Let S be the set of circles in the plane, and let f : S → R be defined by: f(s) = the area of s.

Is f injective? Surjective? Bijective? Explain your answer.

Now let T be the set of circles in the plane whose center is the origin and define g : T → R≥₀ by: g(t) = the length of the circumference of t.

Is g injective? Surjective? Bijective? Explain your answer. Would your answer change if the codomain of g was R? Why or why not?

Next, Let E be the set of ellipses whose major and minor axes cross the origin and define h : E → R≥₀ by:

h(e) = the area of e.

Is h injective? Surjective? Bijective? Explain your answer.

Note: Points are circles with zero radius.