- #1
songoku
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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-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
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