Inverse Functions

An inverse function is a function that ‘reverses’ the actions of the original function.
To find an inverse function, switch the x and y in the equation of the original function.
Ensure to isolate y on one side of the equation to correctly represent the inverse function.
Not all functions have an inverse. Functions only have an inverse if they are one-to-one, that is, for every x, there is exactly one y in the function.
The symbol for the inverse of a function is f^-1(x) – this does not mean 1/f(x).
Graphically, the graph of an inverse function is a reflexion of the original function’s graph over the line y = x.
If f(x) is a function and f^-1(x) its inverse, then f(f^-1(x)) = x and f^-1(f(x)) = x; they ‘reverse’ each other.
Inverse functions are fundamentally related to the idea of reversibility in mathematics.