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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Functions

NDA 2018 · Mathematics · Functions

For f to be a function, what is the domain of f , if f(x)= 1 |x|-x ?

For ff to be a function, what is the domain of ff, if f(x)=1∣x∣−x?f(x)=\frac{1}{\sqrt{|x|-x}} ?

Options

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

Correct answer

A. (−∞,0)(-\infty, 0)

Step-by-step solution

f(x)=1∣x∣−x∣x∣−x>0f(x)=\frac{1}{\sqrt{|x|-x}}|\mathrm{x}|-\mathrm{x} > 0 since the denominator cannot be zero. ∴∣x∣>x\therefore|\mathrm{x}| > \mathrm{x} for x>0,x>xx > 0, x > x is not possible.  for x<0,∣x∣>x⇒2x<0⇒x<0\begin{aligned} & \text{ for } \mathrm{x} < 0,|\mathrm{x}| > \mathrm{x} \\ & \Rightarrow 2 \mathrm{x} < 0 \quad \Rightarrow \mathrm{x} < 0 \end{aligned}\thereforedomainisdomain is(-\infty, 0)$
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