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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]


y=x2+x+2x2+x+1,
y=1+1x2+x+1 [i.e y>1] . . . (i)

yx2+yx+y = x2+x+2
x2 (y - 1) + x(y - 1) + (y - 2) = 0,

xϵ RD0
(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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