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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

Consider the equation x+|y|=2 y . Which of the following statements...

Consider the equation x+∣y∣=2yx+|y|=2 y. Which of the following statements are not correct? 1. yy as a function of xx is not defined for all real xx. 2. yy as a function of xx is not continuous at x=0x=0. 3. yy as a function of xx is differentiable for all xx. Select the correct answer using the code given below.

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1, 2 and 3

Correct answer

D. 1, 2 and 3

Step-by-step solution

x+∣y∣=2yx=2y−∣y∣2y−∣y∣=x2y−y=x [for y≥0 ] y=x2y+y=xfor[y≥0]3y=xy=13xy={xy≥013xy<0 function is defined for  all value of x. or y={x;x≥013x;x<0\begin{aligned} & x+|y|=2 y \\ & x=2 y-|y| \\ & 2 y-|y|=x \\ & 2 y-y=x \\ & \text{ [for } y \geq 0 \text{ ] } \\ & y=x \\ & 2 y+y=x \quad for[y \geq 0]\\ & 3 y=x \\ & y=\frac{1}{3} x \\ & y=\left\{\begin{array}{cc} x & y \geq 0 \\ \frac{1}{3} x & y < 0 \end{array} \text{ function is defined\text{ for } all value of } \mathrm{x} .\right. \\ & \text{ or } \mathrm{y}=\left\{\begin{array}{lll} x ; & x \geq 0 \\ \frac{1}{3} x & ; & x < 0 \end{array}\right. \\ \end{aligned}\thereforebycheckingby checkingyasafunctionofas a function ofxiscontinuousatis continuous atx=0,butnotdifferentiableat, but not differentiable atx=0$. So all of the statements are not correct.
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