Let $ f : X \rightarrow Y $ be a function. If B is subset of y then its inverse image $ f^-B $ is the subset of x define by $ f^-B = {x : f(x) \in B} $ Now prove the following. $ i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1 $ […]

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Inverse function

## If x is a subset of Y then, is inverse of x also a subset of Y?

Let $ f : X \rightarrow Y $ be a function. If B is subset of y then its inverse image $ f^-B $ is the subset of x define by $ f^-B = {x : f(x) \in B} $ Now prove the following. $ i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1 $ […]