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Question

Determine the range of the function f(x)  defined as:
f(x)=x2+x+2x2+x+1,xϵR 
  1. (1,)
  2. (1,117)

     
  3. (1,73]

     
  4. (1,75]
     


Solution

The correct option is C (1,73]

 
Let y = f(x)=x2+x+2x2+x+1,xϵR
y=x2+x+2x2+x+1
y=1+1x2+x+1    [i.e. y>1]    ....(i)
yx2+yx+y=x2+x+2
x2(y1)+x(y1)+(y2)=0,xϵR
Since, x is real, D0
(y1)24(y1)(y2)0(y1){(y1)4(y2)}0(y1)(3y+7)01y73   ....(iii)
From Eqs. (i) and (ii), Rangeϵ(1,73]

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