Inverse Functions

 


Let the function   y=f(x)  be defined as the set of   X  
and have a range  Y.

If the each   y   is the element of   Y  there exists a single value of   x   such that    f(x)=y.

then this correspondence defines a certain function  x=g(y)
called inverse with respect to given function   y=f(x).

The sufficient condition for existence of an inverse is  a strict monotony of the original function
               y=f(x).

If the function increases (decreases), then the inverse function is also decreases (increases).

Graph of the inverse function   x=g(y)  coincides with that of the function   y=f(x)   if the independent variable is marked off along the    y-axis.   If the independent variable is laid off along the   x-axis   i.e. if the inverse function is written in the form    y=g(x),     then the graph of the inverse function will be symmetric to that of the function     y=f(x)    with respect to the bisector of the first and third quadrant.