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Question

Range of the function f(x)=x2+x+2x2+x+1; xϵR is

A
(1, )
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B
(1,117)
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C
(1, 73]
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D
(1, 75)
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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+2x2(y1)+x(y1)+(y2)=0,xϵRD0(y1)24(y1)(y2)0(y1){(y1)4(y2)}0(y1)(3y+7)0
1y73 . . . (ii)
From (i) and (ii), we get
1<y73

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