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Question: Answered & Verified by Expert
Let $A=\{x \in R, x \neq 0,-4 \leq x \leq 4\} \quad$ and $f: A \rightarrow R$ defined by $f(x)=\frac{|x|}{x}$ for $x \in A$. Then, the range of $f$ is
MathematicsFunctionsAP EAMCETAP EAMCET 2002
Options:
  • A $\{1,-1\}$
  • B $\{x: 0 \leq x \leq 1\}$
  • C (1)
  • D $\{x:-4 \leq x \leq 0\}$
Solution:
2694 Upvotes Verified Answer
The correct answer is: $\{1,-1\}$
Since, $x$ lies between -4 and 4 and $f(x)=\frac{|x|}{x}$, then $f(x)$, is either $-\frac{x}{x}$ or $\frac{x}{x}$ as $x < 0$ or $x \geq 0$ $\therefore f(x)$, is either -1 or 1
$$
\therefore \quad R=\{1,-1\}
$$

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