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Let [x] and x denote the greatest integers and the fractional parts of real number x , and f:R-->R , g:R-->R be two functions defined by f(x)=x and g(x)=[x] , then f[g(x)] is equal to.

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Solution:    f(x)=x=(x-[x])      .........(1)

                                  g(x)=[x].                ..........(2)

              Rightarrow         (fog)(x)=f[g(x)]=g(x)-[g(x)],

            Rightarrow           (fog)(x)=[x]-[[x]]=[x]-[x]=0

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Deependra Verma

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