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INVERTIBLE FUNCTIONS
If f is invertible, then f must be one-one and onto and conversely, if f is one-one and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is one-one and onto, especially when the actual inverse of f is not to be determined.
A function f : X → Y is defined to be invertible, if there exists a function g : Y → X such that $$gof= I_X and fog=I_Y$$. The function g is called the inverse of f and is denoted by $$f^{-1}$$.
OR
If a function f defined by f : X → Y and the inverse function defined by $$f^{-1}:Y \rightarrow X$$ then $$f^{-1}of(x)=x$$ and $$fof^{-1}(x)=x$$.