### 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.

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.