Let A= x :x 0-4 4 and f:A be defined by f(x)= |x| x for x Then A: - Vidyadip

MCQ

Let $\text{A}=\{\text{x}\in\text{R}:\text{x}\neq0-4\leq\text{x}\leq4\}$ and $\text{f}:\text{A}\in\text{R}$ be defined by $\text{f(x)}=\frac{|\text{x}|}{\text{x}}$ for $\text{x}\in\text{A}$ Then A:

✓
$[1,-1]$
B
$\big[\text{x}:0\leq\text{x}\leq4\big]$
C
$\{1\}$
D
$\{\text{x}:-4\leq\text{x}\leq0\}$

✓

Answer

Correct option: A.

$[1,-1]$

As, $\text{|x|}=\begin{cases}\text{x},\ \text{x}\geq0\\-\text{x}<0\end{cases}$
So, $\text{f(x)}=\frac{\text{x}}{|\text{x}|}$
When, $\text{x}<0\text{ i.e.,}\text{ x}\in\big[-4,0\big)$
$\text{f(x)}=\frac{\text{x}}{-\text{x}}=-1$
and when, $\text{x}>0\text{ i.e., x}\in\big(0,4\big]$
$\text{f(x)}=\frac{\text{x}}{\text{x}}=1$
So, range $\text{f}=\{-1,1\}$

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