1.

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

Answer» <html><body><p></p>Solution :We have `<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>(x) =[<a href="https://interviewquestions.tuteehub.com/tag/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</a>^(-1)x]` <br/> `Now -x//2le tan^(-1) x le pi//<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>" for x "in R` <br/> `therefore""[tan^(-1)x]=-2,-1,0,1` <br/> `[tan^(-1)x]=-2` <br/> `therefore""-pi//2letn^(-1)xle-1` <br/> `therefore""-oolt-tan1` <br/> `[tan^(-1)x]=-1` <br/> `therefore""-tanletan^(-1)xlt0` <br/> `-tan^(-1)1lexlt0` <br/> `therefore""0letan^(-1)xlt1` <br/> `therefore""0lexlttan1` <br/> `[tan^(-1)x]=1` <br/> `therefore""1letan^(-1)xltpi//2` <br/> `therefore""tan1lexltoo` <br/> So the <a href="https://interviewquestions.tuteehub.com/tag/graph-17327" style="font-weight:bold;" target="_blank" title="Click to know more about GRAPH">GRAPH</a> of `f(x) =[tan^(-1)x]` can be drawn as shwon in the <a href="https://interviewquestions.tuteehub.com/tag/following-463335" style="font-weight:bold;" target="_blank" title="Click to know more about FOLLOWING">FOLLOWING</a> figure.<br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_010_S01.png" width="80%"/></body></html>


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