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AP EAMCET202017 Sep 2020Evening ShiftMathematicsFunctionsActual

For (f(x)= [x] 1+[x] + x 2+3 x ), where ([x] ) denotes the greatest integer function, the domain and range in (R ) are respectively

Options

  1. A(R- -1, -2 3 ) and (R- 1 3 )
  2. B( R - -1, -2 3 ) and ([-1,1] )
  3. C(R-[-1,0) ) and (R- 1 3 )
  4. D( R -[-1,0) ) and ([-1,1] )

Correct answer

D. ( R -[-1,0) ) and ([-1,1] )

Step-by-step solution

As ([x]=-1 ) when (x [-1,0) ). This makes denominator of first part (1+[x]=0 ). Hence, Interval ([-1,0) ) must be excluded from domain set. ( D (f)=R-[-1,0) ) Also at (x=0 ) (which is part of domain), value of function is zero. i.e. (f(0)=0 ) So option (d) is correct.

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