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Let [x] denote the greatest integer less than or equal to x for any real number x. The range of the function f : R → R, defined by f(x) = sin(π[x])/x^2+5 , is
(a) (-1,1)
(b) [-1,1]
© {-1,1}
(D) {0}

    suman , 7 Years ago
    Grade 12th pass
    anser 2 Answers
    Deepak Kumar Shringi
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    Last Activity: 7 Years ago
    sunny
    Hii budy this is an easy question dont get tricked of denomination 
    Finding range of numerator =sin(π[x])
    Through substitution as sin is an increasing function from -1 to 1 
    Sin3π/2=-1 
    Puting x=3π/2=3×π/2=4.34 so 
    x=4.34and  [x]=4 so from question sin(4π)=0
    Now similarily checking greatest integer for x=π/2,π...or any it ,
    Range of sin(π[x])=0 and since numerator is always zero hence function range is 0.
     Quite tired of typing i m new hey if it helped do not forget to give an approval
     
    Last Activity: 7 Years ago
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