Question

Teach me please
Is there any algebraic way to get the inverse of a set.
for example:
f(x) =x^2 Df = {-1,0,1}, Im (f) = all real numbers
A = {-1,1}, B ={0,1} and B is subset of Im(f)
find f(A) and f^- (B)

Answer 1

I know f(A) = {1}
and f^- (B) = {-1,0,1}
but I have to calculate one by one, I don't know how to deal with the whole set
What if B is not just 2 elements, how can I do? :)