1.

Draw the graph of f(x)=[tan^(-1)x]," where "[*]" represents the greatest integer function".

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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