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Question

Range of the expression f(x)=x2+x+1x2x+1, xR is

A
[13,3]
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B
(,13][3,)
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C
(13,3)
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D
R
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Solution

The correct option is A [13,3]
Let y=x2+x+1x2x+1
yx2yx+y=x2+x+1
(y1)x2(y+1)x+(y1)=0

xRΔ0
(y+1)24(y1)20
3y2+10y30
3y210y+30
(3y1)(y3)0
y[13,3]

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