Range

We have the function

y%3D%5Csin%20%5E%7B-1%7D%5Cleft(%5Cfrac%7Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B2%7D%7D%5Cright)

For

y

to be defined

%5Cleft%7C%5Cfrac%7Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B2%7D%7D%5Cright%7C%3C1

which is true for all

x%20%5Cin%20R

Now,

y%3D%5Csin%20%5E%7B-1%7D%5Cleft(%5Cfrac%7Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B2%7D%7D%5Cright)

%5CRightarrow%20%5Cfrac%7Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B2%7D%7D%3D%5Csin%20y

%5CRightarrow%20x%3D%5Csqrt%7B%5Cfrac%7B%5Csin%20y%7D%7B1-%5Csin%20y%7D%7D

For the existance of

x

%5Csin%20y%20%5Cgeq%200

and

1-%5Csin%20y%3E0

%5CRightarrow%200%20%5Cleq%20%5Csin%20y%3C1

$\Rightarrow 0 \leq y

Chapter Questions
1 MCQs