For a suitable chosen real constant a, let the 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 & fof (x)=f(f(x))=f ( a-x a+x )=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^2+a x-a+x=a^2 x+a x^2+a x-x^2 & (a-1) x^2+ (a^2-1 ) x-a(a-1)=0 & (a-1)(x+a)(x-1)=0 & a=1[ as x -a] & f(x)= 1-x 1+x & f (- 1 2 )= 1+ 1 2 1- 1 2 =3 aligned