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UPSC NDA I 2016 Mathematics Solved Paper

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For the next two (2) items that follow :

Consider the curves

f(x)=x\lvert x\rvert-1

and

g(x)=\begin{cases} \frac{3x}{2}, & x>0 \\ 2x, & x\le 0 \end{cases}

[NDA I 2016]

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Question : 12 of 120

Marks: +1, -0

Where do the curves intersect ?

At (2,3) only
At (-1,-2) only
At (2,3) and (-1,-2)
Neither at (2,3) not at (-1,-2)

Solution:

f(x)=x|x|-1

f(x)=\begin{cases} x^2-1 & x \ge 0 \\ -x^2-1 & x \le 0 \end{cases}

g(x)=\begin{cases} \frac{3x}{2} & x > 0 \\ 2x & x \le 0 \end{cases}

Hence

f(x)

and

g(x)

intersects at

(-1,-2)

and

(2,3)

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