JEE Advanced2011MathematicsTrigonometric EquationsActual
Let f(x)=x^2 and g(x)= x for all x R . Then, the set of all x satisfying ( fogogof )(x)=( gogof )(x) , where (f g)(x)=f(g(x)) is
Options
- An , n 0,1,2,
- Bn , n 1,2,
- C2 +2 n , n ,-2,-1,0,1,2,
- D2 n , n ,-2,-1,0,1,2,
Correct answer
B. n , n 1,2,
Step-by-step solution
f(x)=x^2, g(x)= x(g f)(x)= x^2 go(gof) (x)= ( x^2 )(f g g f)(x)= ( ( x^2 ) )^2 Again, (g f)(x)= x^2 (gogof) (x)= ( x^2 ) Given, ( fogogof )(x)=( gogof )(x) ( ( x^2 ) )^2= ( x^2 ) ( x^2 ) ( x^2 )-1 =0 ( x^2 )=0 or ( x^2 )=1 x^2=0 or x^2= 2 x^2=n (i.e. not possible as -1 1 )