Paragraph: Let f(x)=[x] , where [.] is the greatest integer function and g(x)= x be two real valued functions over R . Question: Which of the following statements are correct? 1. (f f)(x)=f(x) . 2. ( gog )(x)=g(x) only when x=0 . 3. (go (fog)) (x) can take only three values. Select the correct answer using the code given below:

Step-by-step solution

aligned & (f f)(x)=[[x]] and f(x)=[x] & Suppose x=0.2 & (f f)(x)=[[0.2]]=[0]=0 & f(x)=[0.2]=0 & f f(x)=f(x) aligned Now, ( gog )(x)= x and g(x)= x At x=0 aligned & ( gog )(x)= 0= 0=0 & g(x)= 0=0 & ( gog )(x)=g(x) at x=0 aligned and this is true for x = np , where n =0,1,2,3,4 . aligned & (f g)(x)=[ x] & (g o(f g))(x)= [ x] & x has value from -1 to 1 & If -1 x 0 & (g o(f g))(x)= (-1)- (-1) & If 0 x 1 & ( go (f g))(x)= (0)= 0 and & If x=1 & ( go (f g))(x)= (1)= 1 aligned