Let f(x)=|x| and g(x)=[x]-1 , where [.] is the greatest integer function. Let h(x)= f(g(x)) g(f(x)) . What is _ x 0- h(x) equal to?

Step-by-step solution

Since, h(x)= f(g(x)) g(f(x)) = f([x]-1) g(|x|) = |[x]-1| [|x|]-1 aligned & Since, = _ x 0- h(x) & = _ x 0⁻ |[x]-1| [x]-1 = _ x 0⁻ = |-1-1| -1 =-2 aligned