Two functions f and g are inverses if they satisfy:
f(g(x)) = x and g(f(x)) = x
If two functions f and g are inverses, then the following properties hold true:
1. The composition of f with g results in the identity function.
2. The composition of g with f results in the identity function.
Formally, if f and g are inverses, then:
1. f(g(x)) = x for all x in the domain of g.
This means that after applying g to x, applying f will take you back to x.
2. g(f(x)) = x for all x in the domain of f.
This means that after applying f to x, applying g will take you back to x.
The inverse of a function f can be denoted as f^(-1) and is defined as the function that satisfies the above two properties. Note that not all functions have inverses. A function must be both one-to-one and onto in order to have an inverse.
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