Inverse Functions

Inverse function

The reversal of a function such that every element in the codomain is mapped to only one element in the domain

If two functions f and g are inverse functions of each other

then, the domain of f=range of g and domain of g=range of f

If two functions f and g are inverse functions of each other

then the graph of g is the reflection of the graph of f at the line y=x

Properties of inverse function (1)

Only restricted to one-to-one function which has inverse function

Properties of inverse function (2)

fg(x)=gf(x)=x, where g(x) is the inverse function of f(x)

Properties of inverse function (3)

Graph of f inverse is the reflection graph of f in the line y=x and vice versa

Properties of inverse function (4)

If the point (a,b) lies on the graph of f then the point (b,a) lies on the graph of f inverse

Step 1 of determining the inverse function

Change function y=f(x) to the form x=f(y)

Step 2 of determining the inverse function

Write as

Step 3 of determining the inverse function

Replace variable y with variable x