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UPSC NDA I 2014 Mathematics Paper

For the next two (02) items that follow:

Consider the function

f(x)=\frac{x^2-x+1}{x^2+x+1}

[NDA I 2014]

Question : 98 of 120

Marks: +1, -0

Solution:

Let

y=\frac{x^2-x+1}{x^2+x+1}

\Rightarrow yx^2+yx+y=x^2-x+1

\Rightarrow (y-1)x^2+(y+1)x+y-1=0

\Rightarrow D=(y+1)^2-4(y-1)^2\geq 0

\Rightarrow (y+1+2y-2)(y+1-2y+2)\geq 0

\Rightarrow (3y-1)(y-3)\leq 0

\Rightarrow \frac{1}{3}\leq y\leq 3

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