Paragraph: Let f(x)=[x] , where [.] is the greatest integer function and g(x)= x be two real valued functions over R . Question: Which one of the following statements is correct?

Step-by-step solution

aligned & (f g)(x)=[ x] & _ x 0⁺ (f o g)(x)= _ x 0⁺ [ x]=[h] where h 0 & _ x 0⁺ (f o g)(x)=0 & _ x 0⁻ (f g)(x)= _ x 0⁻ [ x]=[h] where h 0 & _ x 0⁻ (f o g)(x)=-1 & _ x 0 (f o g)(x) does not exist. aligned Now, (g o f)(x)= [x] aligned & _ x 0⁺ (g o f)(x)= _ x 0⁺ [x]= 0=0 & _ x 0⁻ (g o f)(x)= _ x 0⁻ [x]= (-1)=-0.01745 & _ x 0 (g o f)(x) does not exist. & _ x 0⁺ (f o g)(x)= _ x 0⁺ (g o f)(x) aligned