Given: Let f: X - Y be a function. Then we have an associated function f^(-1): P(Y) - P(X), where f^(-1) (B)⊂X is the inverse image of B⊂Y.

Question

Given: Let f: X -> Y be a function. Then we have an associated function f^(-1): P(Y) -> P(X), where f^(-1) (B)⊂X is the inverse image of B⊂Y.

Question: Show that f^(-1) is one-to-one if and only if f is onto.

[Notes: ⊂ represents subspace, I just couldn’t find a way to put the line under the symbol.
f^(-1) indicates the inverse of f.]