Relations And Functions

We have

A%3D%5Cleft%5C%7B1%2C%200%2C%201%2C%202%5Cright%5C%7D

B%3D%5Cleft%5C%7B4%2C%202%2C%200%2C%202%5Cright%5C%7D

and

f%2C%20g%20%3A%20A%20%5Crightarrow%20B

Now,

f%20%5Cleft(x%5Cright)%3Dx%5E%7B2%7D-x

%5CRightarrow%20f%20%5Cleft(0%5Cright)%3D0-0%3D0

and

f%20%5Cleft(1%5Cright)%3D1-1%3D0%5Cldots%5Cleft(i%5Cright)

and

f%20%5Cleft(2%5Cright)%3D2%5E%7B2%7D-2%3D2

Also,

g%5Cleft(x%5Cright)%3D2%5Cleft%7Cx-%5Cfrac%7B1%7D%7B2%7D%5Cright%7C-1

%5CRightarrow%20g%20%5Cleft(0%5Cright)%3D2%5Cleft%7C%5Cfrac%7B-1%7D%7B2%7D%5Cright%7C-1%3D1-1%3D0

and

g%5Cleft(1%5Cright)%3D2%5Cleft%7C1-%5Cfrac%7B1%7D%7B2%7D%5Cright%7C-1

%3D1-%3D0%20%5Cldots%5Cleft(ii%5Cright)

and

g%20%5Cleft(2%5Cright)%3D2%5Cleft%7C2-%5Cfrac%7B1%7D%7B2%7D%5Cright%7C-1

%3D%5Cfrac%7B2.3%7D%7B2%7D-1%3D2

Hence from Eqs.

%5Cleft(i%5Cright)

and

%5Cleft(ii%5Cright)

, we can say that

f%5Cleft(x%5Cright)%3Dg%5Cleft(x%5Cright)

%5CRightarrow%20f%3Dg

Chapter Questions
4 MCQs