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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 , 6 Years ago
Grade 12th pass
anser 2 Answers
Deepak Kumar Shringi

Last Activity: 6 Years ago

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sunny

Last Activity: 6 Years ago

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
 

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