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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Functions

NDA 2015 · Mathematics · Functions

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

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

Options

  1. A[0,∞)[0, \infty)
  2. B(−∞,0)(-\infty, 0)
  3. C[1,∞)[1, \infty)
  4. D(−∞,0](-\infty, 0]

Correct answer

B. (−∞,0)(-\infty, 0)

Step-by-step solution

f(x)=1∣x∣−x∣x∣−x≠0\begin{aligned} & f(x)=\frac{1}{\sqrt{|x|-x}} \\ & |x|-x \neq 0 \end{aligned} So x<0\mathrm{x} < 0....(1) x=(−∞,0)\mathrm{x}=(-\infty, 0) again ∣x∣−x>0∣x∣>xitispossibleonlywhen|x|-x > 0|\mathrm{x}| > \mathrm{x} it is possible only whenxisnegative.is negative.x=(-\infty, 0)....(2) So from eq.(1)&eq.(2) domain x=eq. (1) \& eq. (2) \text{ domain } \mathrm{x}=(-\infty, 0)
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