For a suitable chosen real constant a , let a function f: R-[-a] R be defined by f(x)= a-x a+x . Further, suppose that for any real number x -a and f(x) -a,(f o f)(x)=x . Then f ( -1 2 ) is equal to

Step-by-step solution

aligned & (f f)(x)= a- a-x a+x a+ a-x a+x =x & a^2+a x-a+x a^2+a x+a-x =x & (a+1) x+ (a^2-a )= (a^2+a ) x+(a-1) x^2 & a+1=a^2+a, a^2-a=0, a-1=0 & a=1 & f(x)= 1-x 1+x & f (- 1 2 )= 1+ 1 2 1- 1 2 =3 aligned