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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

What is the domain of the function f(x)= 1 |x|-x ?

What is the domain of the function f(x)=1∣x∣−xf(x)=\frac{1}{\sqrt{|x|-x}} ?

Options

  1. A(−∞,0)(-\infty, 0)
  2. B(0,∞)(0, \infty)
  3. C0<x<10 < x < 1
  4. Dx>1x > 1

Correct answer

A. (−∞,0)(-\infty, 0)

Step-by-step solution

We know that |x|=\left\{x,x≥0−x,x<0\begin{array}{cc} x, & x \geq 0 \\ -x, & x < 0 \end{array}\right.$ For domain, $|x|-x > 0$ Case 2: $x < 0$ Case 1: $x > 0 \Rightarrow x-x=0$ (not possible)\begin{aligned} & -x-x > 0 \\ & \Rightarrow-2 x > 0 \\ & \Rightarrow x < 0 \end{aligned}$$So,So,x \in(-\infty, 0)$
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