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Draw the graph of f(x)=[tan^(-1)x]," where "[*]" represents the greatest integer function". |
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Answer» Solution :We have `F(x) =[TAN^(-1)x]` `Now -x//2le tan^(-1) x le pi//2" for x "in R` `therefore""[tan^(-1)x]=-2,-1,0,1` `[tan^(-1)x]=-2` `therefore""-pi//2letn^(-1)xle-1` `therefore""-oolt-tan1` `[tan^(-1)x]=-1` `therefore""-tanletan^(-1)xlt0` `-tan^(-1)1lexlt0` `therefore""0letan^(-1)xlt1` `therefore""0lexlttan1` `[tan^(-1)x]=1` `therefore""1letan^(-1)xltpi//2` `therefore""tan1lexltoo` So the GRAPH of `f(x) =[tan^(-1)x]` can be drawn as shwon in the FOLLOWING figure.
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