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Draw the graph of f(x)=[tan^(-1)x]," whe...

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

Text Solution

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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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