What is "inverse function"

n. (context mathematics English) A function that does exactly the opposite of another; formally ''g'' is the inverse function of a function ''f'' if and only if: $forall\; x\; .\; f(x)\; =\; y\; implies\; g(y)\; =\; x$. Notation: $f^\{-1\}$.

n. the function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x

In mathematics, if a function f(x) = y is injective, exactly one function g(y) will exist such that g(y) = x, otherwise no such function will exist. The function g(y) is called the inverse function of f(x) because it "reverses" f(x); that is to say g(f(x)) = x.