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- Homework Statement
- Given that X and Y are nonempty subsets of ℝ and let f : X → Y be a function and f^(-1) (y) = {x ∈ X | f(x) = y}. If A ⊆ X and B ⊆ Y, which statement must be true?

a. f^(-1) (f(A)) ⊆ f(f^(-1) (B))

b. A ⊆ f^(-1) (f(A))

c. f(f^(-1) (B)) = f^(1-) (B)

d. B ⊆ f(f^(-1) (B))

e. f^(-1) (f(A)) ⊆ A

- Relevant Equations
- Inverse function

Composite function

f

For (b), I get A ⊆ A

For (d), I get B ⊆ B

For (e), I get A ⊆ A

So there are three correct statements? Thanks

_{-1}(f(A)) = A and f_{-1}(f(B)) = B so options (a) and (c) are wrong.For (b), I get A ⊆ A

For (d), I get B ⊆ B

For (e), I get A ⊆ A

So there are three correct statements? Thanks