Inverse functions

A function $f$ is called a one-to-one function if it satisfies

$\displaystyle f(a) \neq f(b)$   whenever $ a \neq b$$\displaystyle .

The above condition becomes equivalent to the following: `` $ f(a) = f(b)$ always implies $ a = b$.'' When a function $f$ is a one-to-one function, the inverse function $ g$ can be defined as the function satisfying

$\displaystyle y = f(x)$    if and only if $\displaystyle \quad x = g(y).

We denote the inverse function of $f$ by the symbol $ f^{-1}$.

Domain of $ f^{-1}$. If $f$ is a one-to-one function from the domain $ D$ to the range $ R$, then the inverse function $ f^{-1}$ becomes a one-to-one function from the domain $ R$ to the range $ D$.

Department of Mathematics
Last modified: 2005-09-29