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need solution for RD Sharma maths class 12 chapter 8 Continuity exercise Fill in the blanks question 19

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Answer: All integral points

Hint: f(x) is discontinuous when f(x)  is not defined

Given: f(x)=[x]



            Continuity will be measured at

                    \bulletx is an integer

                    \bullet x is not an integer

            Case I: x is not an integer

                        \begin{aligned} &\lim _{x \rightarrow d} f(x)=f(d) \\ &{[d]=[d]} \end{aligned}

                        f(x)  is continuous at all non-integer

              Case II: x is an integer

                            f(x)=[x] is continuous if LHL=RHL=f(c)

                        \begin{aligned} &\lim _{x \rightarrow c^{-}} f(x)=\lim _{k \rightarrow 0} f(c-h)=c-h=c-1 \\ &\lim _{x \rightarrow c^{+}} f(x)=\lim _{k \rightarrow 0} f(c+h)=c+h=c \\ &c \neq c-1 \\ &L H L \neq R H L \end{aligned}

                        f(x) is discontinuous at all integer



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