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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

Consider the curves f(x)=x|x|-1 and g(x)= cases (3 x)/(2), & x > 0...

Consider the curves f(x)=x∣x∣−1f(x)=x|x|-1 and g(x)=g(x)=\begin{cases}\frac{3 x}{2}, & x > 0 \\ 2 x, & x \leq 0\end{cases}$$ Where do the curves intersect?

Options

  1. AAt (2,3)(2,3) only
  2. BAt (−1,−2)(-1,-2) only
  3. CAt⁡(2,3)\operatorname{At}(2,3) and (−1,−2)(-1,-2)
  4. DNeither at (2,3)(2,3) nor at (−1,−2)(-1,-2)

Correct answer

C. At⁡(2,3)\operatorname{At}(2,3) and (−1,−2)(-1,-2)

Step-by-step solution

f(x)=x∣x∣−1f(x)={x2−1x>0−x2−1x≤0g(x)={3x2x>02xx≤0\begin{aligned} & f(x)=x|x|-1 \\ & f(x)=\left\{\begin{array}{ll} x^2-1 & x \gt 0 \\ -x^2-1 & x \leq 0 \end{array} \quad g(x)= \begin{cases}\frac{3 x}{2} & x \gt 0 \\ 2 x & x \leq 0\end{cases} \right. \end{aligned}
Hence f(x)andg(x)f(x) and g(x) intersects at (−1,−2)and(2,3)(-1,-2) and (2,3).
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