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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Functions

NDA 2024 · Mathematics · Functions

Which one of the following is correct in respect of f(x)= 1 |x|-x...

Which one of the following is correct in respect of f(x)=1∣x∣−xf(x)=\frac{1}{\sqrt{|x|-x}} and g(x)=1x−∣x∣g(x)=\frac{1}{\sqrt{x-|x|}} ?

Options

  1. Af(x)f(x) has some domain and g(x)g(x) has no domain
  2. Bf(x)f(x) has no domain and g(x)g(x) has some domain
  3. Cf(x)f(x) and g(x)g(x) have the same domain
  4. Df(x)f(x) and g(x)g(x) do not have any domain

Correct answer

A. f(x)f(x) has some domain and g(x)g(x) has no domain

Step-by-step solution

f(x)=1∣x∣−x Domain of f(x),∣x∣−x>0⇒x∈(−∞,0)g(x)=1x−∣x∣\begin{gathered}f(x)=\frac{1}{\sqrt{|x|-x}} \\ \text{ Domain of } f(x),|x|-x > 0 \\ \Rightarrow \quad x \in(-\infty, 0) \\ g(x)=\frac{1}{\sqrt{x-|x|}}\end{gathered} Domain of g(x)=x−∣x∣>0⇒∣x∣>xg(x)=x-|x| > 0\Rightarrow \quad|x| > x
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