# Lecture-7 Class 12 Maths

Aim for the moon. If you miss, you may hit a star. – W. Clement Stone

# Lecture - 7 Relations and Functions

INVERTIBLE FUNCTIONS
If f is invertible, then f must be one-one and onto and conversely, if f is one-one and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is one-one and onto, especially when the actual inverse of f is not to be determined.
A function f : X → Y is defined to be invertible, if there exists a function g : Y → X such that $gof= I_X and fog=I_Y$. The function g is called the inverse of f and is denoted by $f^{-1}$.
OR
If a function f defined by f : X → Y and the inverse function defined by $f^{-1}:Y \rightarrow X$ then $f^{-1}of(x)=x$ and $fof^{-1}(x)=x$.