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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Functions

NDA 2013 · Mathematics · Functions

What is the range of the function f(x)=(|x|)/(x), x ≠ 0 ?

What is the range of the function f(x)=∣x∣x,x≠0f(x)=\frac{|x|}{x}, x \neq 0 ?

Options

  1. ASet of all real numbers
  2. BSet of all integers
  3. C{−1,1}\{-1,1\}
  4. D{−1,0,1}\{-1,0,1\}

Correct answer

C. {−1,1}\{-1,1\}

Step-by-step solution

x>0;f(x)=xx=1x<0;f(x)=−xx=−1Range ={−1,1}\begin{aligned} & x > 0 ; f(x)=\frac{x}{x}=1 \\ & x < 0 ; f(x)=-\frac{x}{x}=-1 \\ & \text{Range }=\{-1,1\}\end{aligned}
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