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Drew the graph of y=cos^(-1)sqrt(log_([x])(|x|/x)) where [*] represents the greastest integer function. |
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Answer» SOLUTION :We have `y=f(x)=cos^(-1)sqrt(log_([x])(|x|/x))` `|x|/x={{:(1,xgt0),(-1,XLT0):}` We must have `xgt0` Also` [x]gt0" and "[x]ne1` `therefore""[x]GE2" or "xge2` From (i) and (ii), the domain of the function is `(2, oo)` For`xge2, |x|/x=1` `therefore""log_([x])(|x|/x)=0-(" for "xge2)` `therefore""sqrt(log_([x])(|x|/x))=0(" for "x ge 2)` `therefore""cos^(-1)sqrt(log_([x])(|x|/x))=pi/2` HENCE, GRAPH of `y=f(x)" if the line y"=pi/2" for "x in [2, oo)`.
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