# Inverse Functions

## 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.