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Question Number 25825 by rita1608 last updated on 15/Dec/17

$$f:R\to Risdefinedby$$$$f\left(x\right)=\{\underset{-1ifx\notin Z}{1}\mathrm{if}\mathrm{x}\in Z$$$$Isfcontinuousatx=1andx=-\frac{3}{2}\int ?$$$$$$

Answered by prakash jain last updated on 15/Dec/17

$$\underset{x\to 1^{+}}{\lim }f\left(x\right)=\underset{h\to 0^{+}}{\lim }f(1+h)=-1$$$$\because (1+h)\notin \mathbb{Z}\mathrm{as}h\to 0$$$$\mathrm{similary}$$$$\underset{x\to 1^{-}}{\lim }f\left(x\right)=-1$$$$f\left(1\right)=1$$$$\mathrm{LHL}=\mathrm{RHL}\ne f\left(1\right)\mathrm{function}$$$$\mathrm{is}\mathrm{not}\mathrm{continuius}\mathrm{at}1.$$$$\mathrm{for}3/2$$$$\mathrm{LHL}=\mathrm{RHL}=-1$$$$f\left(3/2\right)=-1$$$$f\left(x\right)\mathrm{is}\mathrm{continous}\mathrm{at}3/2$$

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