If f: R [-1,1] and g: R A are two surjective mappings and (g(x)- 3 )= f(x) 2 4-f^2(x) , then A=

Step-by-step solution

Let f(x)=y , then aligned & (g(x)- 3 )= f(x) 2 4-f^2(x) = y 2 4-y^2 =t (let) & y^2- y^4 4 =t^2 4 y^2-y^4=4 t^2 & (y^2-2^2=-4 t^2+4 t^2=1- 1 4 (y^2-2^2 )^2 . & f(x)=y [-1,1] y^2 [0,1] & t^2 [0, 3 4 ] t [- 3 2 , 3 2 ] & So, (g(x)- 3 ) [- 3 2 , 3 2 ] & g(x)- 3 [- 3 , 3 ] g(x) [0, 2 3 ] aligned