Relations And Functions

Let

f(x)%3Dy%2C

then

%5Csin%20%5Cleft(g(x)-%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright)%3D%5Cfrac%7Bf(x)%7D%7B2%7D%20%5Csqrt%7B4-f%5E%7B2%7D(x)%7D

%3D%5Cfrac%7By%7D%7B2%7D%20%5Csqrt%7B4-y%5E%7B2%7D%7D%3Dt

(let)

%5CRightarrow%20y%5E%7B2%7D-%5Cfrac%7By%5E%7B4%7D%7D%7B4%7D%3Dt%5E%7B2%7D

%5CRightarrow%204%20y%5E%7B2%7D-y%5E%7B4%7D%3D4%20t%5E%7B2%7D

%5CRightarrow%20%5Cleft(y%5E%7B2%7D-2%5Cright)%5E%7B2%7D%3D-4%20t%5E%7B2%7D%2B4

%5CRightarrow%20t%5E%7B2%7D%3D1-%5Cfrac%7B1%7D%7B4%7D%5Cleft(y%5E%7B2%7D-2%5Cright)%5E%7B2%7D

%5Cbecause%20f(x)%3Dy%20%5Cin%5B-1%2C1%5D

%5CRightarrow%20y%5E%7B2%7D%20%5Cin%5B0%2C1%5D

%5Ctherefore%20t%5E%7B2%7D%20%5Cin%5Cleft%5B0%2C%20%5Cfrac%7B3%7D%7B4%7D%5Cright%5D

%5CRightarrow%20t%20%5Cin%5Cleft%5B-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%5D

So,

%5Csin%20%5Cleft(g(x)-%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright)%20%5Cin%5Cleft%5B-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%5D

%5CRightarrow%20g(x)-%5Cfrac%7B%5Cpi%7D%7B3%7D%20%5Cin%5Cleft%5B-%5Cfrac%7B%5Cpi%7D%7B3%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5Cright%5D

%5CRightarrow%20g(x)%20%5Cin%5Cleft%5B0%2C%20%5Cfrac%7B2%20%5Cpi%7D%7B3%7D%5Cright%5D

Chapter Questions
1 MCQs