Hi

It's karamveer

Today in the class we had learned about Inverse of the function.

Inverse of Relations.The inverse of the relation is the set of the ordered pairs

obtained by interchanging the coordinates of each ordered pair in the relation.

Inverse of Functions.The inverse of the function f(x) is also a function.It is called an inverse function of f(x) and is written f^-1(x).

Find the inverse of f(x) = 6x-5

To find the inverse of the function follow these steps.

y = 6x-5

Step.1:Replace f(x) by y

y=6x-5

Step.2:Interchange x and y

x=6y-5

Step.3:Solve for y

6y=x+5

y=x+5/2

Step.4:Replace y with f^-1(x)

Graph the function and its inverse

The graphs of f (x) and f^-1(x) are relate to each other in this way:(a,b) lies onthe graph f then the point (b,a) lies on the graph f^-1 and the vice versa.This means that graph of the f function is a reflection of the graph of f^-1 in the line y=x.

Second example I want to show the one how would you determine that f(x) and g(x) are the inverses of each other

Example.1f(x)=2x-5 or

Solution :The function f(x) and g(x) are the inverses of each other if f(g(x))=x and g(f(x))=x.

And...

So that's means.They are the inverses of each other.

Make sure you'll try n doing Example no. 5 on page 14 in the booklet.

Good Evening to everyone.See you all tomorrow@10.30.